CONTENTS OF ALL VOLUMES of “FCAA” Vol. 1 (1998) – Vol. 17 ...fcaa/CONTENTS_FCAA_ALL.pdf · CONTENTS OF ALL VOLUMES of “FCAA” Vol. 1 (1998) – Vol. 17 (2014) Managing Editor:

CONTENTS OF ALL VOLUMES of “FCAA”

Vol. 1 (1998) – Vol. 17 (2014)

Managing Editor: Virginia Kiryakova

Published by: De Gruyter Open (former Versita) and SpringerFounding Publisher (1998): Inst. of Math. and Inform. – Bulg. Acad. Sci.

Available at http://www.math.bas.bg/∼fcaa (1998–2010),http://link.springer.com/journal/13540 (since 2011)

http://www.math.bas.bg/~fcaa

http://link.springer.com/journal/13540

EDITORIAL BOARD

Managing Editor: Virginia Kiryakova

Editorial OfficeInstitute of Mathematics and Informatics – Bulgarian Academy of Sciences

“Acad. Georgi Bontchev” Str., Block 8, Sofia – 1113, BulgariaE-mail: [email protected] , [email protected] ; Fax: +359-2-9478608

Honorary Founding Editors ‡

Anatoly A. Kilbas (Belarus) Gary F. Roach (UK)Eric R. Love (Australia) Ian N. Sneddon (UK)

Honorary Editors

Paul Butzer (Germany) Megumi Saigo (Japan)Michele Caputo (Italy) Stefan Samko (Portugal)Rudolf Gorenflo (Germany) Jerome Spanier (USA)Shyam L. Kalla (India) Hari M. Srivastava (Canada)D. Przeworska-Rolewicz (Poland) Bogoljub Stankovic (Serbia)

Members of Editorial Board

Boris Baeumer (N. Zealand) Piotr Mikusinski (USA)Dumitru Baleanu (Turkey) Juan J. Nieto (Spain)Lyubomir Boyadjiev (Bulgaria) Ivo Petras (Slovak R.)Yury Brychkov (Russia) Igor Podlubny (Slovak R.)Wen Chen (China) Sergei Rogosin (Belarus)Kai Diethelm (Germany) Boris Rubin (USA)Ivan Dimovski (Bulgaria) Peter Rusev (Bulgaria)Neville Ford (UK) Jocelyn Sabatier (France)Alan Freed (USA) Enrico Scalas (Italy)Rudolf Hilfer (Germany) Jose A. TenreiroMourad Ismail (USA) Machado (Portugal)Ravi N. Kalia (USA) Juan J. Trujillo (Spain)Anatoly Kochubei (Ukraine) Sabir Umarov (USA)Yury Luchko (Germany) Blas Vinagre (Spain)Richard Magin (USA) Vu Kim Tuan (USA)Francesco Mainardi (Italy) YangQuan Chen (USA)Oleg Marichev (USA) Ahmed Zayed (USA)

Technical Assistant: Stefan Kiryakov (Diogenes Co., Bulgaria)i

ISSN 1311-0454 FCAA, Vol. 1, No 1 (1998)

Contents

Preface

D. Przeworska-RolewiczCARLEMAN OPERATORS IN COMMUTATIVE ALGEBRASWITH LOGARITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Bl. Sendov, P. MarinovBINARY EXPONENTIAL FRACTAL FUNCTIONS . . . . . . . . . . . . . . . . . 23

L. Galue, S. L. KallaSOME RECURRENCE RELATIONS FOR THE GENERALIZEDHYPERGEOMETRIC FUNCTIONS OF THE GAUSS TYPE . . . . . . . . 49

Yu. Luchko, R. GorenfloSCALE-INVARIANT SOLUTIONS OF A PARTIAL DIFFERENTIALEQUATION OF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

V. S. Kiryakova, M. Saigo, H. M. SrivastavaSOME CRITERIA FOR UNIVALENCE OF ANALYTIC FUNCTIONSINVOLVING GENERALIZED FRACTIONAL CALCULUSOPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Information on International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . .105

Addresses of the EB Members

Order Form, Subscription Details

2

ISSN 1311-0454 FCAA, Vol. 1, No 2 (1998)

Contents

G. G. Walter, A. I. ZayedMULTIRESOLUTION ANALYSIS WITH SAMPLING SUBSPACES 109

C. A. M. van Berkel, J. de GraafTHE FOURIER-JACOBI TRANSFORM OF ANALYTIC FUNCTIONSWHICH ARE (ALMOST) PERIODIC IN THE IMAGINARYDIRECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

A. A. Kilbas, B. Bonilla, M. Rivero, J. Rodriguez, J. TrujilloCOMPOSITIONS OF BESSEL TYPE INTEGRAL TRANSFORMWITH FRACTIONAL OPERATORS ON SPACES Fp,µ AND F ′

p,µ . . 135

P. RusevON THE ASYMPTOTICS OF THE WEBER-HERMITE FUNCTIONIN THE COMPLEX PLANE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

R. Gorenflo, F. MainardiRANDOM WALK MODELS FOR SPACE-FRACTIONALDIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

B. RubinFRACTIONAL CALCULUS AND WAVELET TRANSFORMSIN INTEGRAL GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

Information on International Meetings . . . . . . . . . . . . . . . . . . . . . 192, 220

Proceedings “TMSF, Varna’96” (Contents) . . . . . . . . . . . . . . . . . . . . 221

Addresses of the EB Members

Order Form, Subscription Details

3

ISSN 1311-0454 FCAA, Vol. 1, No 3 (1998)

Contents

S. SamkoA NEW APPROACH TO THE INVERSIONOF THE RIESZ POTENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . 225

V. M. Almeida, J. RodrıguezAN ALGEBRAIC DERIVATIVE AND SOME OFITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

E. BazhlekovaTHE ABSTRACT CAUCHY PROBLEM FORTHE FRACTIONAL EVOLUTION EQUATION . . . . . . . . . . . . . . . . . . . . 255

M. L. Glasser, A. A. Al-JarrahSOME SONINE-GEGENBAUER INTEGRALS . . . . . . . . . . . . . . . . . . . . . 271

G. R. MillerSHIFT OPERATORS AND FRACTIONAL CALCULUS . . . . . . . . . . . . 279

S. B. Yakubovich, L. D. GusarevichON THE NON-CONVOLUTION TRANSFORMATION WITHTHE MACDONALD TYPE KERNEL FUNCTION . . . . . . . . . . . . . . . . . 297

Jae Ho ChoiUNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTSINVOLVING A CERTAIN FRACTIONAL INTEGRAL OPERATORAND ITS PARTIAL SUMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Information on International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . 319

Proceedings of International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . 321

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

4

ISSN 1311-0454 FCAA, Vol. 1, No 4 (1998)

Contents

B. StankovicS-BOUNDED FOURIER HYPERFUNCTIONS . . . . . . . . . . . . . . . . . . . . . 327R. K. Raina, R. N. KaliaCHARACTERIZATIONS FOR SUBCLASSES OF ANALYTICFUNCTIONS CONNECTING LINEAR FRACTIONALCALCULUS OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334S. KempfleCAUSALITY CRITERIA FOR SOLUTIONS OFLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . 351I. A. Aliev, S. BayrakciON INVERSION OF B-ELLIPTIC POTENTIALS BYTHE METHOD OF BALAKRISHNAN-RUBIN . . . . . . . . . . . . . . . . . . . . . 365L. Boyadjiev, H.-J. DobnerON THE SOLUTION OF A FRACTIONALFREE ELECTRON LASER EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385N. Sudland, G. Baumann, T. F. NonnenmacherOPEN PROBLEM: WHO KNOWS ABOUT THE ℵ-FUNCTIONS ? 401O. Marichev, M. TrottTHE MATHEMATICAL FUNCTIONS OF MATHEMATICA(Announce for a POSTER) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403Djrbashian Memorial Conference (DMC98)(Erevan, Sept. 10-12, 1998; M. M. Djrabshian 1918-1994) . . . . . . . . . . . . 409Colloquium FRACTIONAL DIFFERENTIAL SYSTEMS(Paris, December 3-4, 1998; Information) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415Internat. Conference on Scientific Computations(Beirut, March 15-17, 1999; ICS99) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417Session on FUNCTION SPACES AND APPL-S(Fukuoka, August 16-21, 1999; at Internat. Congress ISAAC99) . . . . . 4193rd Internat. Workshop TMSF, AUBG’99(Blagoevgrad (Bulgaria), August 13-20, 1999) . . . . . . . . . . . . . . . . . . . . . . . 421Addresses of the EB Members, Order Form FCAA . . . . . . . . . . . 425Contents of Vol.1, No 1 - No 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

5ISSN 1311-0454 FCAA, Vol. 2, No 1 (1999)

Contents

A. Oustaloup, J. Sabatier, P. LanusseFROM FRACTAL ROBUSTNESS TO THE CRONE CONTROL . . . . 1A. DenisjukINTEGRAL GEOMETRY ON THE FAMILY OF SEMI-SPHERES . . 31B. RubinLp-PROPERTIES OF SOLUTIONS OF THE SINGULARHELMHOLTZ EQUATION IN THE HALF-SPACE . . . . . . . . . . . . . . . . . . 47S. SamkoSOME REMARKS ON THE AUTHOR’S PAPER “A NEW APPROACHTO THE INVERSION OF THE RIESZ POTENTIAL OPERATOR” 63N. Karapetiants, S. SamkoMULTI-DIMENSIONAL INTEGRAL OPERATORSWITH HOMOGENEOUS KERNELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67E. Moiseev, K. Skornik, W. KieratLIFE AND WORK OF PROF. A.P. PRUDNIKOV . . . . . . . . . . . . . . . . . . 97A. Kilbas, S. SamkoA.P. PRUDNIKOV: A NOTE IN MEMORIAM . . . . . . . . . . . . . . . . . . . . . . 107A. Carpinteri, F. Mainardi (Ed-s)FRACTALS AND FRACTIONAL CALCULUS INCONTINUUM MECHANICS (Annotation of a Proceedings) . . . . . . . . . 109I. Podlubny (Author)FRACTIONAL DIFFERENTIAL EQUATIONS:An Introduction to . . . (Annotation of a New Book) . . . . . . . . . . . . . . . . . . 113R. Hilfer (Editor)APPLICATIONS OF FRACTIONAL CALCULUS IN PHYSICS(Annotation of a New Volume) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Informations on International Meetings“TMSF,AUBG’99”, “AMADE’99”, “AART’99” . . . . . 123, 125, 127Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Contents of Vol.1 (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6ISSN 1311-0454 FCAA, Vol. 2, No 2 (1999)

Contents

Vu Kim TuanPALEY-WIENER-TYPE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135M.L. Glasser, M.E.H. IsmailA CURIOUS EXPRESSION FOR THE WEYLFRACTIONAL INTEGRAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145D. Przeworska-RolewiczISOMORPHISMS PRESERVING LEIBNIZ CONDITION . . . . . . . . . . . 149R. Gorenflo, Yu. Luchko, P.P. ZabrejkoON SOLVABILITY OF LINEAR FRACTIONAL DIFFERENTIALEQUATIONS IN BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163N.K. Karapetiants, L.D. ShankishviliA SHORT PROOF OF HARDY-LITTLEWOOD-TYPETHEOREM FOR FRACTIONAL INTEGRALS INWEIGHTED HOLDER SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177A.N. Karapetyants, E. Ramırez de ArellanoCHARACTERIZATION OF ANISOTROPIC LIZORKIN-TYPEMIXED NORM SPACES GENERATED BY DEGENERATEDIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193V.A. Nogin, S.G. SamkoSOME APPLICATIONS OF POTENTIALS ANDAPPROXIMATIVE INVERSE OPERATORS INMULTI-DIMENSIONAL FRACTIONAL CALCULUS . . . . . . . . . . . . . . . 205

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

7ISSN 1311-0454 FCAA, Vol. 2, No 3 (1999)

Contents

N. VirchenkoON SOME GENERALIZATIONS OF THE FUNCTIONSOF HYPERGEOMETRIC TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233F. Levron, J. Sabatier, A. Oustaloup, L. HabsiegerFROM PARTIAL DIFFERENTIAL EQUATIONSOF PROPAGATIVE RECURSIVE SYSTEMSTO NON INTEGER DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . 245I. AlievON THE BOCHNER-RIESZ SUMMABILITYAND RESTORATION OF µ-SMOOTH FUNCTIONSBY MEANS OF THEIR FOURIER TRANSFORMS . . . . . . . . . . . . . . . . . 265R.M. Peat, W.J. Spratt & A.C. McBrideSPACES OF SMOOTH FUNCTIONS ON R+ FORMELLIN MULTIPLIER TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277R.M. Peat, A.C. McBrideSPACES OF SMOOTH FUNCTIONS ON Rn

VIA SPHERICAL HARMONICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289K. DiethelmESTIMATION OF QUADRATURE ERRORS IN TERMSOF CAPUTO-TYPE FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . 313N.G. Samko, S.G. SamkoON APPROXIMATIVE DEFINITIONOF FRACTIONAL DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . .329A.A. Kilbas, J.J. TrujilloON THE HANKEL-TYPE INTEGRAL TRANSFORMIN Lν,r-SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343International MeetingsVIII INTERNATIONAL M. CRAVCHUK CONFERENCE . . . . . . . . . . .354Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

8

ISSN 1311-0454 FCAA, Vol. 2, No 4 (1999)

Proc. of the 4th International Workshop

“TMSF,AUBG’99”, Part A

Contents

Preface

E. BazhlekovaPERTURBATION PROPERTIES FOR ABSTRACT EVOLUTIONEQUATIONS OF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . .359

L.T. DechevskyATOMIC DECOMPOSITION OF FUNCTION SPACES ANDFRACTIONAL INTEGRAL AND DIFFERENTIAL OPERATORS . . 367

R. Gorenflo, Yu. Luchko, F. MainardiANALYTICAL PROPERTIES AND APPLICATIONSOF THE WRIGHT FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

S. Kempfle, I. SchaeferFUNCTIONAL CALCULUS METHODVERSUS RIEMANN-LIOUVILLE APPROACH . . . . . . . . . . . . . . . . . . . . . 415

A.A. Kilbas, M. Saigo, A. BorovcoON THE LOMMEL-MAITLAND TRANSFORM IN Lν,r-SPACE . . . . 429

V. KiryakovaMULTIINDEX MITTAG-LEFFLER FUNCTIONS,RELATED GELFOND-LEONTIEV OPERATORSAND LAPLACE TYPE INTEGRAL TRANSFORMS . . . . . . . . . . . . . . . . 445

Yu. LuchkoOPERATIONAL METHOD IN FRACTIONAL CALCULUS . . . . . . . . .463

S.T. MinchevaON THE AUTOMORPHISMS OF L1 COMMUTINGWITH A GENERALIZED INTEGRATION OPERATOR . . . . . . . . . . . . 489

9

A.H. Al-Shammery, S.L. Kalla, H.G. KhajahA FRACTIONAL GENERALIZATIONOF THE FREE ELECTRON LASER EQUATION . . . . . . . . . . . . . . . . . . .501

K. SkornikMIKUSINSKI’S OPERATIONAL CALCULUSAND ITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

N. VirchenkoON A GENERALIZED LAGUERRE’S FUNCTIONAND ITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529

M. ZahleFRACTIONAL INTEGRALS AND DERIVATIVESWITH RESPECT TO A MEASURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

H.M. SrivastavaBook’s Review: FRACTIONAL DIFFERENTIAL EQUATIONSby I. Podlubny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543

Reports on International MeetingsAART (Sept. 21-25, 1999, Warsaw) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

Reports on International MeetingsAMADE (Sept. 14-18, 1999, Minsk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549


Participants in the “TMSF,AUBG’99” Workshop . . . . . . . . . . . . . 553

10

ISSN 1311-0454 FCAA, Vol. 2, No 5 (1999)

Proc. of the 4th International Workshop

“TMSF,AUBG’99”, Part B

Contents

Preface

M.B. Abd-el-Malek, F.H. Michael, A.H. TwefickNONLINEAR GRAVITY WAVES OVERIRREGULAR BOTTOM VIA PERTURBATION METHOD . . . . . . . . . 555

F. Al-Sirehy, B. FisherTHE COMPOSITION OF THE FUNCTIONS |x|−λ AND |x|2r/λ . . . . 575

G.I. Balikov, I.P. DimitrovSOME NOTES ON ZAHARIUTA-VOGT’S CONDITIONS . . . . . . . . . . 583

G.I. Chobanov, I.H. DimovskiA TWO-VARIATE OPERATIONAL CALCULUSFOR BOUNDARY VALUE PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .591

J. Chung, S.-Y. Chung, D. Kim, H. KimTRIGONOMETRIC SERIES ANDALMOST PERIODIC GENERALIZED FUNCTIONS . . . . . . . . . . . . . . . 603

Soon-Yeong ChungA TEMPERATURE TRANSFORM ANDA BIHARMONIC ANALYSIS ON TEMPERATURES . . . . . . . . . . . . . . . 613

S.-Y. Chung, D. Kim, Y. YeomSTIELTJES MOMENT PROBLEMFOR GEL’FAND-LEONTIEV SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

I.P. DimitrovABOUT OVERCONVERGENT FUNCTIONAL SERIES INTHE SPACE OF ANALYTIC FUNCTIONS IN THE UNIT DISK . . . 631

S.B. DomaMOMENTS OF INERTIA OF DEFORMED NUCLEI . . . . . . . . . . . . . . . 637

A.M. HamzehDESIGN CONSIDERATIONS AND COMPUTATIONALMETHODS FOR ESTIMATION OF RATIOS . . . . . . . . . . . . . . . . . . . . . . . 651

11

A. Kaminski, D. Perisic, S. PilipovicTHE CONVOLUTION AND CONVOLUTORS INGEL’FAND-SHILOV SPACES OF DISTRIBUTIONS . . . . . . . . . . . . . . . . 657

E. Malkowsky, E. SavasMATRIX TRANSFORMATIONS IN SOME SPACESOF ALMOST SUMMABLE AND BOUNDED SEQUENCES . . . . . . . . 669

M.I. MitrevaTAME EXTENSION OPERATORS FOR HERMITE’SINTERPOLATION PROBLEM ON ANALYTIC VARIETES . . . . . . . . 679

J. Paneva-KonovskaA TAUBER TYPE THEOREMFOR SERIES IN BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683

P. RusevPERRON’S TYPE ASYMPTOTIC FORMULASFOR THE LAGUERRE POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

M. Salameh, A.N. El-Kassar, R.E. Ghattas, B.S. MaddahTHE CONTINUOUS REVIEW INVENTORYMODEL, A MODIFIED APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699

M. SkwarczynskiON COMPLETENESS OF INFINITELYCONNECTED DOMAINS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

T. StoyanovABOUT A PROBLEM OF OBRESHKOFF . . . . . . . . . . . . . . . . . . . . . . . . . . 717

N. TuneskiA NOTE ON SOME SIMPLE SUFFICIENT CONDITIONSFOR UNIVALENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721

V. VatchevTURAN QUADRATURES FOR FOURIER COEFFICIENTSAND POLYNOMIALS OF MINIMAL DEVIATION . . . . . . . . . . . . . . . . . 729



Participants in the “TMSF,AUBG’99” Workshop . . . . . . . . . . . . . 743

12ISSN 1311-0454 FCAA, Vol. 3, No 1 (2000)

Contents

Om P. AgrawalA GENERAL SOLUTION FOR THE FOURTH-ORDERFRACTIONAL DIFFUSION-WAVE EQUATION . . . . . . . . . . . . . . . . . . . . . 1A. MeskhiON THE BOUNDEDNESS AND COMPACTNESS OF BALLFRACTIONAL INTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 13D. Przeworska-RolewiczNULLITY, DEFICIENCY AND COMMUTATORS OFLINEAR, LOGARITHMIC AND ANTILOGARITHMIC MAPPINGS 31W. WyssTHE FRACTIONAL BLACK-SCHOLES EQUATION . . . . . . . . . . . . . . . . 51R.B. Paris, G.V. LiakhovetskiASYMPTOTICS OF THE MULTIDIMENSIONALFAXEN INTEGRAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63R. Gorenflo, A. Iskenderov, Yu. LuchkoMAPPING BETWEEN SOLUTIONS OF FRACTIONALDIFFUSION-WAVE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75V.A. Nogin, P.A. LuzhetskayaINVERSION AND DESCRIPTION OF THE RANGESOF MULTIPLIER OPERATORS OFSTRICHARTZ–PERAL–MIYACHI-TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Kluwer Acad. Publishers:ENCYCLOPAEDIA OF MATHEMATICS (Info and Reprinted Items) 97D. Przeworska-Rolewicz, ALGEBRAIC ANALYSIS . . . . . . . . . . . . . . . 100B. Rubin, CALDERON-TYPE REPRODUCING FORMULA . . . . . . .103

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Contents of Vol. 1 and Vol. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

13ISSN 1311-0454 FCAA, Vol. 3, No 2 (2000)

Contents

A.W. Niukkanen, V.I. Perevozchikov, V.A. LurieA GENERALIZATION OF A CLASSICAL RELATION BETWEENJν+n(z), Jν(z) and Jν−1(z) WITH COMMENTS ONTHE MODERN STATE AND TRENDS IN SPECIAL FUNCTIONS 119Nguyen Minh Chuong, Ta Ngoc TriTHE INTEGRAL WAVELET TRANSFORM IN Lp(Rn), 1 ≤ p ≤ ∞ 133A.N. Karapetyants, E. Ramırez de ArellanoON THE INVERSION OF POTENTIAL TYPE OPERATORSWITH KERNELS HAVING SINGULARITIES ON A SPHERE . . . . . 141L. Galue, I. Ali, S.L. KallaAN EXTENSION OF THE LAGUERRE POLYNOMIALSAND ASSOCIATED ORTHONORMAL FUNCTIONS . . . . . . . . . . . . . . 161U. SkornikA REMARK ON ELEMENTS OF D′

Lq(R) ASBOUNDARY VALUES OF HOLOMORPHIC FUNCTIONS . . . . . . . . 173B. RubinGENERALIZED MINKOWSKI-FUNK TRANSFORMS AND SMALLDENOMINATORS ON THE SPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

New Book from World Scientific Publ.:PARTIAL DIFFERENTIAL EQUATIONS, An Introduction withMathematica and Maple, by I.P. Stavroulakis, S. Tersian . . . . . . . . . . . . 205Old Book from Longman 7→ CRC Press:GENERALIZED FRACTIONAL CALCULUS AND APPLICATIONS,by V. Kiryakova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

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E.G. BazhlekovaSUBORDINATION PRINCIPLE FOR FRACTIONALEVOLUTION EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213B. M. Vinagre, I. Podlubny, A. Hernandez, V. FeliuSOME APPROXIMATIONSOF FRACTIONAL ORDER OPERATORSUSED IN CONTROL THEORY AND APPLICATIONS . . . . . . . . . . . . 231R. Gorenflo, Yu.F. Luchko, S.R. UmarovON THE CAUCHY AND MULTI-POINT PROBLEMSFOR PARTIAL PSEUDO-DIFFERENTIAL EQUATIONSOF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249D. Przeworska-RolewiczSPECIAL FUNCTIONS AS ANTILOGARITHMSOF SECOND ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277N.M. Atakishiyev, M.K. AtakishiyevaON A SIMPLE INTEGRAL REPRESENTATIONOF THE CONTINUOUS q-HERMITE POLYNOMIALS . . . . . . . . . . . . 297F. Al-Musallam, Vu Kim TuanA CLASS OF CONVOLUTION TRANSFORMATIONS . . . . . . . . . . . . 303Open Problem: ARITHMETICAL PROPERTIES OFGEGENBAUER POLYNOMIALS . . . , by B. Rubin . . . . . . . . . . . . . . . . 315Corrigenda: LETTER, by S. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Corrigenda: CORRECTIONS to paper: “A two-variate operational . . . ”,FCAA 2, No 5 (1999), 591-601, by G.I. Chobanov, I.H. Dimovski . . . . 318

Anniversary: 60th ANNIVERSARY of Professor H.M. Srivastava . 319

Meetings: 3rd Internat. ISAAC Congress (Berlin, 2001) . . . . . . . . . . . . . 327Meetings: Internat. Conf. ”AMADE-2001” (Minsk) . . . . . . . . . . . . . . . . . 333Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

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Anniversary: 70th ANNIVERSARY of Professor R. GORENFLONew Website: FRACALMOLetters by V. Kiryakova, A. Kilbas and S. Samko, O. Marichev . . . . . . 339CV and List of Publications of R. Gorenflo . . . . . . . . . . . . . . . . . . . . . . . . . . 343

Vu Kim Tuan, Dinh Thanh DucAUTOMATIC EVALUATION OF AN ABSCISSA OFCONVERGENCE FOR INVERSE LAPLACE TRANSFORM . . . . . . 353I. PodlubnyMATRIX APPROACH TO DISCRETE FRACTIONAL CALCULUS 359S. Kempfle, I. SchaferFRACTIONAL DIFFERENTIAL EQUATIONSAND INITIAL CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387S.G. Samko, B.G. VakulovON EQUIVALENT NORMS IN FRACTIONAL ORDERFUNCTION SPACES OF CONTINUOUS FUNCTIONSON THE UNIT SPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401B. RubinFRACTIONAL DIFFERENTIATION ANDSPHERICAL RADON TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435A.A. Kilbas, S.V. DemiankoSOLUTION OF MULTI-DIMENSIONAL ABEL-TYPE INTEGRALEQUATIONS WITH POWER-LOGARITHMIC KERNELS . . . . . . . . . 439R. Gorenflo, Yu.F. Luchko, S.R. UmarovON SOME BOUNDARY VALUE PROBLEMSFOR PSEUDO-DIFFERENTIAL EQUATIONS WITHBOUNDARY OPERATORS OF FRACTIONAL ORDER . . . . . . . . . . . 453

In Memoriam: Prof. IAN N. SNEDDON (08.12.1919-04.11.2000) . . 469Notes by V. Kiryakova, A. McBride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Meetings: “OPSFA”, Roma, June 18-22, 2001 . . . . . . . . . . . . . . . . . . . . . 438Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

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V. Kokilashvili, A. MeskhiFRACTIONAL INTEGRALS ON MEASURE SPACES . . . . . . . . . . . . . . 1P. Mikusinski, M. MorimotoBOEHMIANS ON THE SPHERE AND THEIR SPHERICALHARMONIC EXPANSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25G.D. Handley, J.J. Koliha, J. PecaricHILBERT-PACHPATTE TYPE INTEGRAL INEQUALITIESFOR FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37J. A. Tenreiro MachadoDISCRETE-TIME FRACTIONAL-ORDER CONTROLLERS . . . . . . . 47A.P. Chegolin, V.A. NoginON THE L - CHARACTERISTIC OF SOME MULTIPLIEROPERATORS WITH OSCILLATING SYMBOLSIN THE NON-ELLIPTIC CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67F.M. Hafez, A.M.A. El-Sayed, M.A. El-TawilON A STOCHASTIC FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . 81S.L. Kalla, B.N. Al-SaqabiFURTHER RESULTS ON A UNIFIED FORMOF GAMMA-TYPE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91B.G. Vakulov, N.K. Karapetiants, L.D. ShankishviliSPHERICAL HYPERSINGULAR OPERATORSOF IMAGINARY ORDER AND THEIR MULTIPLIERS . . . . . . . . . . . . 101

Anniversary: 60th ANNIVERSARY of Professor S. SAMKOLetters by the Editor, N. Karapetiants and A. Kilbas, B. Rubin . . . . . . 113CV and List of Publications of S. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Meetings: “Constructive Function Theory 2002”, Varna, Bulgaria . . 36Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

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Tae Sik Kim, Seunghwan KimRELATIONS BETWEEN DIMENSIONS ANDDIFFERENTIABILITY OF CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Nguyen Minh Chuong, Bui Kien CuongGALERKIN-WAVELET APPROXIMATION FOR A CLASSOF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS . . . . . . . . . . 143F. Mainardi, Yu. Luchko, G. PagniniTHE FUNDAMENTAL SOLUTION OFTHE SPACE-TIME FRACTIONAL DIFFUSION EQUATION . . . . . . 153D. Przeworska-RolewiczRIEMANN-HILBERT TYPE PROBLEMS WITH INVOLUTIONSIN LEIBNIZ ALGEBRAS WITH LOGARITHMS . . . . . . . . . . . . . . . . . . . 193G.F. RoachWAVE SCATTERINGBY TIME DEPENDENT PERTURBATIONS . . . . . . . . . . . . . . . . . . . . . . 209I. Dimovski, K. SkornikMEAN-PERIODIC OPERATIONAL CALCULI. SINGULAR CASES . . .237I. Dimovski, A. Kaminski, S. MinchevaTHE COMMUTANT OF AN INTEGRATION OPERATORWITH MULTIPOINT FUNCTIONAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Anniversary: 70th ANNIVERSARY ofProfessor Danuta PRZEWORSKA-ROLEWICZLetters by the Editor and K. Skornik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255CV and List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

Meetings: “Analytical Methods of Analysis and Differential Equations”(AMADE-2001), Minsk, Belarus, February 15-19, 2001 . . . . . . . . . . . . . . 267Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269Order Form, Subscription Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

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M. M. Wyss, W. WyssEVOLUTION, ITS FRACTIONAL EXTENSIONAND GENERALIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273K. M. Kolwankar, J. Levy VehelMEASURING FUNCTIONS SMOOTHNESS WITHLOCAL FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285M. Aslam Chaudhry, S. M. ZubairEXTENDED GAMMA AND DIGAMMA FUNCTIONS . . . . . . . . . . . . 303S. R. Umarov, E. M. SaydamatovON THE SPECTRUM OF GENERALPSEUDO-DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . 327V. A. Nogin, D. N. KarausevON THE L-CHARACTERISTIC OF SOME POTENTIAL -TYPE OPERATORS WITH RADIAL KERNELS,HAVING SINGULARITIES ON A SPHERE . . . . . . . . . . . . . . . . . . . . . . . . 343Jae Ho Choi, Yong Chan Kim, S. OwaFRACTIONAL CALCULUS OPERATOR AND ITSAPPLICATIONS IN THE UNIVALENT FUNCTIONS . . . . . . . . . . . . . 367L. Boyadjiev, S. L. KallaSERIES REPRESENTATIONS OF ANALYTIC FUNCTIONSAND APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Anniversary: 70th ANNIVERSARY of Professor Peter RUSEV . . . . 409

New Books: by H.M. Srivastava and J. Choi . . . . . . . . . . . . . . . . . . . . . . 302by M Aslam Chaudhry and S.M Zubair . . . . . . . . . . . . . . 325

Addresses of EB Members, Order Form, Subscriptions . . . . . . 417

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M. CaputoDISTRIBUTED ORDER DIFFERENTIAL EQUATIONSMODELLING DIELECTRIC INDUCTION AND DIFFUSION . . . . . 421H. Mejjaoli, Kh. TrimecheHARMONIC ANALYSIS ASSOCIATED WITHTHE DUNKL-BESSEL LAPLACE OPERATORAND A MEAN VALUE PROPERTY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443B. Baeumer, M.M. MeerschaertSTOCHASTIC SOLUTIONS FOR FRACTIONALCAUCHY PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481B. Stankovic, T.M. AtanackovicON A MODEL OF A VISCOELASTIC ROD . . . . . . . . . . . . . . . . . . . . . . . 501S. Samko, M. YakhshiboevON A CLASS OF IDENTITY APPROXIMATIONOPERATORS OF A NON-CONVOLUTION TYPE . . . . . . . . . . . . . . . . 523K. Diethelm, N.J. FordNUMERICAL SOLUTION METHODS FORDISTRIBUTED ORDER DIFFERENTIAL EQUATIONS . . . . . . . . . . 531Yu.A. BrychkovA GENERALIZATION OF THE COOKE’S DUPLICATIONFORMULAS FOR BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 543In Memoriam: Prof. E.R. LOVE (31.03.1912-7.08.2001) . . . . . . . . . . . 549Obituary by J.F. Clark, Note by Editor . . . . . . . . . . . . . . . . . . . . . . . . 550, 551A note in memoriam by A. Kilbas, S. Samko . . . . . . . . . . . . . . . . . . . . . . . . 552

Books: by N. Virchenko, I. Fedotova, “Generalized Associated ... ” 555by U. Trottenberg, C.W. Oosterlee, A. Schuller, “Multigrid” 557

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558, 559, 562, 563


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A. Jouini, K. TrimecheGENERALIZED WAVELET PACKETS AND APPLICATIONTO THE INVERSION OF THE J.L. LIONSTRANSMUTATION OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

M.M. Meerschaert, H.-P. SchefflerSEMISTABLE LEVY MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

L. de Rosa, A. de la TorreON CONDITIONS FOR THE BOUNDEDNESSOF THE WEYL FRACTIONAL INTEGRALIN THE CASE 1 < q ≤ p < ∞ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55G. Dattoli, P.E. Ricci, C. CesaranoDIFFERENTIAL EQUATIONS FORAPPELL TYPE POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

N. Jacob, A. M. KragelohFELLER SEMIGROUPS ON C∞(Rn × T 1) GENERATED BYWEYL FRACTIONAL DERIVATIVESAND PSEUDO-DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . 77

Book’s Review, by V. A. Nogin, for:HYPERSINGULAR INTEGRALS AND THEIRAPPLICATIONS, by Stefan G. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Letter to Editor, by S. G. Samko:Prof. N. KARAPETIANTS’s 60th BIRTHDAY . . . . . . . . . . . . . . . . . . . . . . 123


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D.N. KarasevLp → Lq - ESTIMATES FOR SOME POTENTIAL-TYPEOPERATORS WITH OSCILLATING KERNELS . . . . . . . . . . . . . . . . . . . 131A.A. Rousan, E. Malkawi, E.M. Rabei, H. WidyanAPPLICATIONS OF FRACTIONAL CALCULUSTO GRAVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155P.K. Banerji, L. Debnath, G.M. ShenanAPPLICATION OF FRACTIONAL DERIVATIVEOPERATORS TO THE MAPPING PROPERTIESOF ANALYTIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169V. Karunakaran, R. RoopkumarULTRA BOEHMIANSAND THEIR FOURIER TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 181D. Przeworska-RolewiczBINOMIALS FORMULAEIN COMMUTATIVE LEIBNIZ ALGEBRAS WITH LOGARITHMS 195A.A. Kilbas, E.K. SchetnikovichGENERALIZED HANKEL-TYPE INTEGRAL TRANSFORMON Lν,r-SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Archives: B. L. J. BraaksmaIN MEMORIAM C. S. MEIJER (originally publ. in“Nieuw Archief voor Wiskunde (3)”, XXIII (1975), 95-104) . . . . . . . . . . 227

Letter to Editor, by S. G. Samko:CONGRATULATIONS TO VIRGINIA KIRYAKOVAON HER 5Oth ANNIVERSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245, 249


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V. Kokilashvili, A. MeskhiWEIGHT INEQUALITIES FOR ONE–SIDED POTENTIALSFOR CRITICAL WEIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

H. Irmak, G. Tinaztepe, Y.C. Kim, J.H. ChoiCERTAIN CLASSES AND INEQUALITIES INVOLVINGFRACTIONAL CALCULUSAND MULTIVALENT FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

A. YakubovFRACTIONAL TYPE INTEGRATION OPERATORS INWEIGHTED GENERALIZED HOLDER SPACES . . . . . . . . . . . . . . . . . . 275

N. K. KarapetiantsON BEHAVIOUR OF THE NORMS OF FRACTIONALINTEGRALS OF LARGE ORDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

N.E. Cho, S.Y. Woo, S. OwaUNIFORM CONVEXITY PROPERTIESFOR HYPERGEOMETRIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 303

D.N. Karasev, V.A. NoginDESCRIPTION OF THE RANGES OF SOMEPOTENTIAL-TYPE OPERATORS WITH OSCILLATINGKERNELS IN THE NON-ELLIPTIC CASE . . . . . . . . . . . . . . . . . . . . . . . . 315

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266, 314

Addresses of EB Members, Order Form, Subscriptions 351 - 354

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Anniversary: 60th ANNIVERSARY of Professor F. MAINARDICONGRATULATIONS, LIST OF PUBLICATIONS . . . . . . . . . . . . . . . . 357I. PodlubnyGEOMETRIC AND PHYSICAL INTERPRETATIONOF FRACTIONAL INTEGRATION ANDFRACTIONAL DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Vu Kim Tuan, Dinh Thanh DucA NEW REAL INVERSION FORMULA OF THELAPLACE TRANSFORM AND ITS CONVERGENCE RATE . . . . . . 387N. Jacob, A. M. KragelohTHE CAPUTO DERIVATIVE, FELLER SEMIGROUPS,AND THE FRACTIONAL POWER OFTHE FIRST ORDER DERIVATIVE ON C∞(R+

0 ) . . . . . . . . . . . . . . . . . . 395S. Kempfle, I. Schafer, H. BeyerFUNCTIONAL CALCULUS AND A LINKTO FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411E. BazhlekovaSTRICT Lp SOLUTIONSFOR FRACTIONAL EVOLUTION EQUATIONS . . . . . . . . . . . . . . . . . . 427A.A. Kilbas, M. Saigo, J.J. TrujilloON THE GENERALIZED WRIGHT FUNCTION . . . . . . . . . . . . . . . . . . 437O. V. Doubrovina, S. V. RogosinON LINEAR AND NONLINEAR INTEGRAL EQUATIONSON FINITE INTERVALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461H.M. SrivastavaSOME FAMILIES OF MULTIVARIABLE BIORTHOGONALPOLYNOMIALS AND ASSOCIATEDGENERATING FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479R. Gorenflo, J. Loutchko, Yu. LuchkoCOMPUTATION OF THE MITTAG-LEFFLER FUNCTIONEα,β(z) AND ITS DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

International Meeting: AMADE-2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519Addresses of EB Members, Order Form, Subscriptions 521 - 524

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A. Oustaloup, V. Pommier, P. LanusseDESIGN OF A FRACTIONAL CONTROLUSING PERFORMANCE CONTOURS.APPLICATION TO AN ELECTROMECHANICAL SYSTEM . . . . . . . 1B. RubinNOTES ON RADON TRANSFORMSIN INTEGRAL GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25J. A. Tenreiro MachadoA PROBABILISTIC INTERPRETATION OFTHE FRACTIONAL-ORDER DIFFERENTIATION . . . . . . . . . . . . . . . . . 73P. RusevA NOTE ON JONQUIERE POLYNOMOALS . . . . . . . . . . . . . . . . . . . . . . . 81Yu. V. Vasil’evMODIFIED WHITTAKER TRANSFORMON Lν,r-SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Corrections: to Figure 4 in:“GEOMETRIC AND PHYSICAL INTERPRETATION . . . ”,FCAA 5, No 4 (2002), 367-386, by I. Podlubny . . . . . . . . . . . . . . . . . . . . . . 109Corrections: to paper“COMPUTATION OF THE MITTAG-LEFFLER FUNCTION . . . ”,FCAA 5, No 4 (2002), 491-518,by R. Gorenflo, J. Loutchko, Y. Luchko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

International Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

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L. DebnathFRACTIONAL INTEGRAL AND FRACTIONALDIFFERENTIAL EQUATIONS IN FLUID MECHANICS . . . . . . . . . 119

V. V. Anh, R. McVinishCOMPLETELY MONOTONE PROPERTYOF FRACTIONAL GREEN FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 157

F. Al-MusallamTHE RANGE OF FINITE INTEGRAL TRANSFORMSARISING FROM n-th ORDER SINGULARSELF-ADJOINT DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . 175

L. Beghin, E. OrsingherTHE TELEGRAPH PROCESS STOPPEDAT STABLE-DISTRIBUTED TIMES AND ITS CONNECTIONWITH THE FRACTIONAL TELEGRAPH EQUATION . . . . . . . . . . . . 187

I. Petras, L. DorcakFRACTIONAL-ORDER CONTROL SYSTEMS:MODELLING AND SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

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S. G. Samko, R. P. CardosoSONINE INTEGRAL EQUATIONSOF THE FIRST KIND IN Lp(0, b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V. Yu. GoncharDISTRIBUTED ORDER TIME FRACTIONALDIFFUSION EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

H.M. Srivastava, A.K. Mishra, M.K. DasA CLASS OF PARABOLIC STARLIKE FUNCTIONSDEFINED BY MEANS OF A CERTAINFRACTIONAL DERIVATIVE OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . 281

J. Paneva-KonovskaCOMPLETE SYSTEMS OF BESSEL FUNCTIONS OFFIRST KIND IN SPACES OF HOLOMORPHIC FUNCTIONS . . . . . 299

A. AlmeidaINVERSION OF THE RIESZ POTENTIAL OPERATORON LEBESGUE SPACES WITH VARIABLE EXPONENT . . . . . . . . . 311

International MeetingsSecond Announcement and Call for Papers forFirst IFAC Workshop on “FDA’04, Bordeaux, France” . . . . . . . . . . . . . . 329


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Anniversary: 75th ANNIVERSARY of Professor P.L. BUTZER . . . 333Anniversary: 70th ANNIVERSARY of Professor G.F. ROACH . . . . 341S. SamkoHARDY INEQUALITY INTHE GENERALIZED LEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . 355A.A. Kilbas, M. Rivero, J.J. TrujilloEXISTENCE AND UNIQUENESS THEOREMS FORDIFFERENTIAL EQUATIONS OF FRACTIONAL ORDERIN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS . . . . . . . . 363D. Przeworska-RolewiczRICCATI TYPE EQUATIONS INLEIBNIZ ALGEBRAS WITH LOGARITHMS . . . . . . . . . . . . . . . . . . . . . . 401S. SamkoHARDY-LITTLEWOOD-STEIN-WEISS INEQUALITY INTHE LEBESGUE SPACES WITH VARIABLE EXPONENT . . . . . . . 421F. Mainardi, G. Pagnini, R. GorenfloMELLIN TRANSFORM AND SUBORDINATION LAWSIN FRACTIONAL DIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . 441V. Kokilashvili, A. MeskhiON A TRACE INEQUALITY FOR ONE-SIDED POTENTIALSWITH MULTIPLE KERNELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461V.B. Shakhmurov, A.I. ZayedFRACTIONAL WIGNER DISTRIBUTIONAND AMBIGUITY FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473P. RusevCORRIGENDUM to my paper in: “FCAA”, vol. 6, No 1 (2003)“A NOTE ON JONQUIERE POLYNOMOALS” . . . . . . . . . . . . . . . . . . . . 491Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

28ISSN 1311-0454 FCAA, Vol. 7, No 1 (2004)

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A.A. Al-JarrahLp-ESTIMATES OF ROUGH INTEGRAL OPERATORSWITH KERNELS INVOLVING BESSEL FUNCTIONS . . . . . . . . . . . . . . 1B. Stankovic, T.M. AtanackovicON AN INEQUALITY ARISING IN FRACTIONALOSCILLATOR THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11L. Debnath, D.D. BhattaSOLUTIONS TO FEW LINEAR FRACTIONALINHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONSIN FLUID MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21N.B. Salem, A.O.A. SalemSOBOLEV TYPE SPACES ASSOCIATEDWITH THE JACOBI-DUNKL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . 37M.M. Meerschaert, J. Mortensen, H.-P. SchefflerVECTOR GRUNWALD FORMULA FORFRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Report on 3rd International Conference”Analytic Methods of Analysis and Differential Equations”(AMADE’ 2003) – Minsk, Belarus, Sept. 4-9, 2003 . . . . . . . . . . . . . . . . . . . 83

Report on 4th International Symposium‘Transform Methods & Special Functions, Borovets’ 2003”(TMSF, Borovets’ 2003) – Borovets, Bulgaria, Sept. 15-21, 2003 . . . . . 86

Contents of “FCAA”Volume 1 (1998) – Volume 6 (2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89


29ISSN 1311-0454 FCAA, Vol. 7, No 2 (2004)

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R.S. Barbosa, J.A.Tenreiro Machado, I.M. FerreiraPID CONTROLLER TUNINGUSING FRACTIONAL CALCULUS CONCEPTS . . . . . . . . . . . . . . . . . . 119R.K. Saxena, T.F. NonnenmacherAPPLICATION OF THE H-FUNCTION IN MARKOVIANAND NON-MARKOVIAN CHAIN MODELS . . . . . . . . . . . . . . . . . . . . . . . 135V. KnopovaON SOME OPERATORS WITH COMPLEX-VALUEDCONTINUOUS NEGATIVE DEFINITE SYMBOLWHICH ARE GENERATORSOF Lp-SUB-MARKOVIAN SEMIGROUPS . . . . . . . . . . . . . . . . . . . . . . . . . 149G. Dattoli, M. Migliorati, H.M. SrivastavaA CLASS OF BESSEL SUMMATION FORMULASAND ASSOCIATED OPERATIONAL METHODS . . . . . . . . . . . . . . . . . 169A.I. KheyfitsCLOSED-FORM REPRESENTATIONSOF THE LAMBERT W FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177K. Diethelm, M. WeilbeerA NUMERICAL APPROACH FOR JOULIN’S MODELOF A POINT SOURCE INITIATED FLAME . . . . . . . . . . . . . . . . . . . . . . 191M.A. Betilgiriev, D.N. Karasev, V.A. NoginLp − Lq - ESTIMATES FOR SOME FRACTIONAL TYPEOPERATORS WITH OSCILLATING KERNELS . . . . . . . . . . . . . . . . . . 213


30ISSN 1311-0454 FCAA, Vol. 7, No 3 (2004)

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Anniversary: 70th ANNIVERSARY of Professor Ivan DIMOVSKI 245

Y. Ben Nakhi and S.L. KallaON SOME MIXTURE DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 261

D. Przeworska-RolewiczPOWERS AND LOGARITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

A.A. Kilbas, S.A. MarzanCAUCHY PROBLEM FOR DIFFERENTIAL EQUATIONWITH CAPUTO DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Minh KhoaA GENERALIZED CONVOLUTION WITHA WEIGHT FUNCTION FOR THE FOURIERCOSINE AND SINE TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

Yu. LuchkoOPERATIONAL RULES FOR A MIXED OPERATOROF THE ERDELYI-KOBER TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

T. M. Atanackovic, B. StankovicAN EXPANSION FORMULA FOR FRACTIONALDERIVATIVES AND ITS APPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . 365

31ISSN 1311-0454 FCAA, Vol. 7, No 4 (2004)

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M. Jelassi, L.T. RachdiON THE RANGE OF THE FOURIER TRANSFORMASSOCIATED WITH THE SPHERICAL MEAN OPERATOR . . . . . 379J. A. Tenreiro Machado, I. S. JesusSUGGESTION FROM THE PAST? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403N. Sudland, G. BaumannON THE MELLIN TRANSFORMS OF DIRAC’SDELTA FUNCTION, THE HAUSDORFF DIMENSIONFUNCTION, AND THE THEOREM BY MELLIN . . . . . . . . . . . . . . . . . 409M. Assal, H. Ben AbdallahCAUCHY PROBLEM FOR DIFFERENTIAL EQUATIONWITH CAPUTO DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .N.K. Karapetyants †, N. SamkoWEIGHTED THEOREMS ON FRACTIONAL INTEGRALSIN THE GENERALIZED HOLDER SPACESVIA INDICES mω AND Mω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M. D. Ortigueira, F. CoitoFROM DIFFERENCES TO DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In Memoriam: Prof. John Boersma (1937 – 2004)OBITUARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

In Memoriam: Prof. Nikolai Karapetyants (1942 – 2005)OBITUARY by Ya. Erusalimskii, A. Kilbas, V. Kokilashvili, V.Rabinovich, V. Kokilashvili, S. Samko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Meetings: AMADE’2006, Second Announcement . . . . . . . . . . . . . . . . . . . . . .

Addresses of EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

32ISSN 1311-0454 FCAA, Vol. 8, No 1 (2005)

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Anniversary: 80th ANNIVERSARY of Acad. B. STANKOVIC,Part 1 (pp. 1 - 66) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

F. Mainardi, R. Gorenflo, A. VivoliRENEWAL PROCESSESOF MITTAG-LEFFLER AND WRIGHT TYPE . . . . . . . . . . . . . . . . . . . . . . 7S. SamkoBEST CONSTANT IN THE WEIGHTED HARDY INEQUALITY:THE SPATIAL AND SPHERICAL VERSION . . . . . . . . . . . . . . . . . . . . . . . 39I. Schafer, S. Kempfle, B. NolteLINEAR FRACTIONAL PDE,UNIQUENESS OF GLOBAL SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 53P. RusevA NOTE ON A CLASSICAL GENERATING FUNCTIONFOR THE JACOBI POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

New Book: by Anatolii A. Kilbas and Megumi Saigo,“H - TRANSFORMS. Theory and Applications”, CRC Press, 2004 . . . 67New Book: by George M. Zaslavsky, “HamiltonianChaos and Fractional Dynamics”, Oxford Univ. Press, 2004 . . . . . . . . . . 69Meetings: “International Symposium on Analytic FunctionTheory, Fractional Calculus and Their Applications”, in honourof 65th Birth Anniversary of Prof. H.M. Srivastava, August 2005 . . . . . 71Corrigenda: Correction to name of R.K. Saxena, in paper:“Application of the H-function in . . . ” in FCAA 7, No 2 (2004),133-148, by R. K. Saxena and Theo F. Nonnenmacher . . . . . . . . . . . . . . . . 72

S. Umarov, R. GorenfloON MULTI-DIMENSIONAL RANDOM WALK MODELSAPPROXIMATING SYMMETRIC SPACE-FRACTIONALDIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

33ISSN 1311-0454 FCAA, Vol. 8, No 2 (2005)

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Anniversary: 80th ANNIVERSARY of Acad. B. STANKOVIC,Part 2 (Collection of papers by Guest-Editor S. Samko) . . . . . . . . . . . . . . 89

N. Jacob, V. KnopovaFRACTIONAL DERIVATIVES AND FRACTIONAL POWERSAS TOOLS IN UNDERSTANDING WENTZELL BOUNDARYVALUE PROBLEMS FOR PSEUDO-DIFFERENTIAL OPERATORSGENERATING MARKOV PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.A. KilbasFRACTIONAL CALCULUS OF THE GENERALIZEDWRIGHT FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113H.J. Seybold, R. HilferNUMERICAL RESULTS FOR THE GENERALIZEDMITTAG-LEFFLER FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127R.K. Saxena, M. SaigoCERTAIN PROPERTIES OF FRACTIONAL CALCULUSOPERATORS ASSOCIATED WITHGENERALIZED MITTAG-LEFFLER FUNCTION . . . . . . . . . . . . . . . . . 141A.N. Karapetyants, D.N. Karasev, V.A. NoginLP → LQ-ESTIMATES FOR THE FRACTIONALACOUSTIC POTENTIALS ANDSOME RELATED OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155R. Gorenflo, E. A. Abdel-RehimDISCRETE MODELS OF TIME-FRACTIONAL DIFFUSIONIN A POTENTIAL WELL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173C. Martınez, M. Sanz, A. RedondoFRACTIONAL POWERS OF ALMOSTNON-NEGATIVE OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201


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A. Al-SalmanROUGH MAXIMAL OSCILLATORY SINGULARINTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

M. Bezzarga, Kh. KefiON A SINGULAR VALUE PROBLEM FORTHE FRACTIONAL LAPLACIAN ON THE EXTERIOROF THE UNIT BALL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

J.D. Griffiths, G.M. Leonenko, J.E. WilliamsGENERALIZATION OF THE MODIFIED BESSELFUNCTION AND ITS GENERATING FUNCTION . . . . . . . . . . . . . . . . 267

A. KhelifiASYMPTOTIC PROPERTY OF EIGENVALUESAND EIGENFUNCTIONS OF THE LAPLACE OPERATORIN DOMAIN WITH A PERTURBED BOUNDARY . . . . . . . . . . . . . . . . 277

L. KamounAN LP − LQ−VERSION OF MORGAN’S THEOREMASSOCIATED WITHPARTIAL DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . 299

S.L. Kalla, R.K. Yadav, S.D. PurohitON THE RIEMANN-LIOUVILLE FRACTIONALq-INTEGRAL OPERATOR INVOLVING A BASICANALOGUE OF FOX H-FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

M. Ilic, F. Liu, I. Turner, V. AnhNUMERICAL APPROXIMATION OFA FRACTIONAL-IN-SPACE DIFFUSION EQUATION, I . . . . . . . . . . 323

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H. Wysocki, M. ZellmaAN ABSTRACT SECOND KIND FREDHOLMINTEGRAL EQUATION WITH DEGENERATED KERNEL . . . . . . . 343P.J. MianaCONVOLUTION PRODUCTS IN L1(R+),INTEGRAL TRANSFORMS AND FRACTIONAL CALCULUS . . . . 361B. Baeumer, S. Kurita, M.M. MeerschaertINHOMOGENEOUS FRACTIONALDIFFUSION EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Anniversary: 65th ANNIVERSARY of Prof. H.M. Srivastava . . . . . . 387

H. Rafeiro, S. SamkoON MULTIDIMENSIONAL ANALOGUE OF MARCHAUDFORMULA FOR FRACTIONAL RIESZ-TYPE DERIVATIVESIN DOMAINS IN Rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393A.A. Kilbas, J.J. Trujillo, A.A. VoroshilovCAUCHY-TYPE PROBLEM FOR DIFFUSION-WAVEEQUATION WITH THE RIEMANN-LIOUVILLEPARTIAL DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403B. E. Gogovcheva, L. BoyadjievFRACTIONAL EXTENSIONS OF JACOBI POLYNOMIALSAND GAUSS HYPERGEOMETRIC FUNCTION . . . . . . . . . . . . . . . . . . 431

Anniversary: 60th ANNIVERSARY of Prof. O.I. Marichev . . . . . . . . 439

36ISSN 1311-0454 FCAA, Vol. 9, No 1 (2006)

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E.M. SaydamatovWELL-POSEDNESS OF THE CAUCHY PROBLEMFOR INHOMOGENEOUS TIME-FRACTIONALPSEUDO-DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 1V.S. Guliyev, J.J. HasanovSOBOLEV-MORREY TYPE INEQUALITY FOR RIESZPOTENTIALS, ASSOCIATED WITH THE LAPLACE-BESSELDIFFERENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17A.A. Rousan, N.Y. Ayoub, F.Y. Alzoubi, H. Khateeb,M. Al-Qadi, M.K. Hasan(Qaseer), B.A. AlbissA FRACTIONAL LC −RC CIRCUIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33C. Abdelkefi, M. SifiON THE UNIFORM CONVERGENCE OF PARTIAL DUNKLINTEGRALS IN BESOV-DUNKL SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . 43S. Umarov, E. SaydamatovA FRACTIONAL ANALOG OF THE DUHAMEL PRINCIPLE . . . . . 57

NEW BOOK: by A. Kilbas, H.M. Srivastava and J.J. Trujillo”THEORY AND APPLICATIONS OF FRACTIONALDIFFERENTIAL EQUATIONS”,Elsevier, North-Holland Mathematics Studies, 204 . . . . . . . . . . . . . . . . . . . 71


37ISSN 1311-0454 FCAA, Vol. 9, No 2 (2006)

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Anniversary: 70th ANNIVERSARY of Prof. Megumi SAIGO . . . . . . 79

I.H. Dimovski, K.A. SkornikOPERATIONAL CALCULI FOR THE EULER OPERATOR . . . . . . . 89N. VirchenkoON THE GENERALIZED CONFLUENTHYPERGEOMETRIC FUNCTION AND ITS APPLICATION . . . . . 101A.A. Kilbas, R.K. Saxena, J.J. TrujilloKRATZEL FUNCTION AS A FUNCTIONOF HYPERGEOMETRIC TYPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109S. S. Eker, H. O. Guney, Sh. OwaON INTEGRAL MEANS FOR FRACTIONAL CALCULUSOPERATORS OF MULTIVALENT FUNCTIONS . . . . . . . . . . . . . . . . . . 133J.E. Pecaric, M. Rodic Lipanovic, H.M. SrivastavaSOME MEAN-VALUE THEOREMS OF THE CAUCHY TYPE . . . . 143V. KiryakovaON TWO SAIGO’S FRACTIONAL INTEGRAL OPERATORSIN THE CLASS OF UNIVALENT FUNCTIONS . . . . . . . . . . . . . . . . . . . 159

Report on the Book: by Anatolii A. Kilbas and Megumi Saigo,“H-TRANSFORMS. THEORY AND APPLICATIONS”,CRC Press, 2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177


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Anniversary: 60th ANNIVERSARY of Prof. Khalifa TRIMECHE 181

I. Dimovski, V. Hristov, M. SifiCOMMUTANTS OF THE DUNKL OPERATORS IN C(R) . . . . . . . . 195N. Ben Salem, A. Ould Ahmed Salemy and B. SelmiMEAN-PERIODIC FUNCTIONS ASSOCIATEDWITH THE JACOBI-DUNKL OPERATOR ON IR . . . . . . . . . . . . . . . . . 215M. Assal, R. BouguilaGENERALIZED SOBOLEV SPACES OF EXPONENTIALTYPE ASSOCIATED WITH THE DUNKL OPERATORS . . . . . . . . . 237H. MejjaoliAN ANALOGUE OF BEURLING-HORMANDER’STHEOREM FOR THE DUNKL-BESSEL TRANSFORM . . . . . . . . . . . 247H. Mabroukq-HEAT OPERATOR AND q-POISSON’S OPERATOR . . . . . . . . . . . . 265A. Gasmi, M. Sifi, F. SoltaniHERZ-TYPE HARDY SPACES FOR THE DUNKLOPERATOR ON THE REAL LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287V.S. Guliyev, M. AssalON MAXIMAL FUNCTION ONTHE LAGUERRE HYPERGROUP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

New Book: by Peter Popivanov, “GEOMETRICAL METHODSFOR SOLVING OF FULLY NONLINEARPARTIAL DIFFERENTIAL EQUATIONS”, UBM’ 2006 . . . . . . . . . . . . 319

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A. K. Mishra, P. GochhayatAPPLICATIONS OF THE OWA-SRIVASTAVA OPERATORTO THE CLASS OF k-UNIFORMLY CONVEX FUNCTIONS . . . . . 323M. Ilic, F. Liu, I. Turner, V. AnhNUMERICAL APPROXIMATION OF AFRACTIONAL-IN-SPACE DIFFUSION EQUATION (II)– WITH NONHOMOGENEOUS BOUNDARY CONDITIONS . . . . . . 333E. Andries, S. Umarov, S. SteinbergMONTE CARLO RANDOM WALK SIMULATIONS BASEDON DISTRIBUTED ORDER DIFFERENTIAL EQUATIONSWITH APPLICATIONS TO CELL BIOLOGY . . . . . . . . . . . . . . . . . . . . . 351M. HaddadHANKEL TRANSFORM IN QUANTUM CALCULUSAND APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Corrigendum: Errata in the paper:“ON INTEGRAL MEANS FOR FRACTIONAL CALCULUSOPERATORS . . . ”, in FCAA 9, No 2 (2006), pp. 133-142,by S. S. Eker, H. O. Guney, Sh. Owa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Meetings: FDA’2006: Report, Program of the Workshop . . . . . . . . . . . 387Meetings: AMADE’2006: Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398Meetings: ICHAA’2006: Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401Meetings: ASME’2007, Announcement: ”Classicand Fractional Dynamics on Continuous and DiscontinuousVector Fields”, Las Vegas, September 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . 405IMI - BAS: Periodicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

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L. Diening, S. SamkoHARDY INEQUALITY IN VARIABLE EXPONENTLEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1H. Mejjaoli, K. TrimecheSPECTRUM OF FUNCTIONSFOR THE DUNKL TRANSFORM ON IRd . . . . . . . . . . . . . . . . . . . . . . . . . . 19M.S. Ben Hammouda, A. NemriPOLYNOMIAL EXPANSIONS FOR SOLUTIONS OFHIGHER-ORDER BESSEL HEAT EQUATIONIN QUANTUM CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39J. Paneva-KonovskaTHEOREMS ON THE CONVERGENCE OF SERIESIN GENERALIZED LOMMEL-WRIGHT FUNCTIONS . . . . . . . . . . . . . 59L. BoyadjievSOME FRACTIONAL EXTENSIONS OFTHE TEMPERATURE FIELD PROBLEM IN OIL STRATA . . . . . . . 75

Meetings: ”FDA’2008”, Fractional Differentiation andits Applications, Ankara (Turkey), 5 - 7 November 2008Invitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99News: Version 6.0 of MATHEMATICAWolfram Research, Inc. - Press Release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101New Book: INTEGRAL TRANSFORMS AND THEIRAPPLICATIONS (2nd Ed.), by L. Debnath and D. Bhatta . . . . . . . . . . 105New Book: THE ART OF MODELING IN SCIENCE ANDENGINEERING WITH MATHEMATICA (2nd Ed.),by D. Basmadjian and R. Farnood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

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Yu.A. Rossikhin, M.V. ShitikovaCOMPARATIVE ANALYSIS OF VISCOELASTIC MODELSINVOLVING FRACTIONAL DERIVATIVESOF DIFFERENT ORDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111R. BagleyON THE EQUIVALENCE OF THE RIEMANN-LIOUVILLEAND THE CAPUTO FRACTIONAL ORDER DERIVATIVESIN MODELING OF LINEAR VISCOELASTIC MATERIALS . . . . . . . 123Z. TomovskiINTEGRAL REPRESENTATIONS OF GENERALIZED MATHIEUSERIES VIA MITTAG-LEFFLER TYPE FUNCTIONS . . . . . . . . . . . . . 127T.M. Atanackovic, B. StankovicON A DIFFERENTIAL EQUATION WITHLEFT AND RIGHT FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . 139K. DiethelmSMOOTHNESS PROPERTIES OF SOLUTIONS OF CAPUTO-TYPE FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . 151M. Yamada, T. Matsuura, S. SaitohREPRESENTATIONS OF INVERSE FUNCTIONS BYTHE INTEGRAL TRANSFORM WITH THE SIGN KERNEL . . . . . . 161M. Zamani, M. Karimi-Ghartemani, N. SadatiFOPID CONTROLLER DESIGN FOR ROBUST PERFORMANCEUSING PARTICLE SWARM OPTIMIZATION . . . . . . . . . . . . . . . . . . . . . 169S.D. Purohit, S.L. KallaON q-LAPLACE TRANSFORMS OFTHE q-BESSEL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Meetings: ”MIA 2008 Conference”, In honour of Prof. J. Pecaric,June 8-14, 2008, Split-Croatia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Meetings 2007 – 2008: Letter by J.A. Tenreiro Machado . . . . . . . . . . 199Meetings: ”FDA’2008”, Fractional Differentiation and its Applications,

November 5-7, 2008, Ankara-Turkey; News: Awards Announced . . 200

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Anniversary: 40 YEARS OF CAPUTO DERIVATIVE AND80th ANNIVERSARY of Prof. Michele CAPUTO: . . . . . . . . . . . . . . . . . . 201Congratulating addresses, Foreword (by F. Mainardi)CV and Selected Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

A.D. Freed, K. DiethelmCAPUTO DERIVATIVES IN VISCOELASTICITY:A NON-LINEAR FINITE-DEFORMATION THEORYFOR TISSUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Y. Luchko, J.J. TrujilloCAPUTO-TYPE MODIFICATIONOF THE ERDELYI-KOBER FRACTIONAL DERIVATIVE . . . . . . . . 249

F. Mainardi, R. GorenfloTIME-FRACTIONAL DERIVATIVESIN RELAXATION PROCESSES:A TUTORIAL SURVEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

M. Caputo, F. MainardiA NEW DISSIPATION MODEL BASED ON MEMORY MECHANISM:REPRINTED PAPER from the journal“Pure and Applied Geophysics (PAGEOPH)”,vol. 91, No 1 (1971), pp. 134-147 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

International Conference: “APPCOM’08”Approximation & Computation (Nis, Serbia, Aug. 25-29, 2008)Dedicated to 60th Anniversary of Prof. Gradimir Milovanovic . . . . . . 325

Web Project: FRACALMO(FRActional CALculus MOdelling), Updated . . . . . . . . . . . . . . . . . . . . . . 326

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A. Fitouhi, N. Bettaibi, W. BinousINVERSION FORMULAS FOR THEq-RIEMANN-LIOUVILLE AND q-WEYL TRANSFORMSUSING WAVELETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

S.K. Sunanda, C. Nahak, S. NandaWITHDRAWN by the Managing Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

P.M. Rajkovic, S.D. Marinkovic, M.S. StankovicON q–ANALOGUES OF CAPUTO DERIVATIVEAND MITTAG–LEFFLER FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

J. L. Da Silva, M. Erraoui, H. OuerdianeGENERALIZED FRACTIONAL EVOLUTION EQUATION . . . . . . 375

H. Rafeiro, S. SamkoON A CLASS OF FRACTIONAL TYPE INTEGRALEQUATIONS IN VARIABLE EXPONENT SPACES . . . . . . . . . . . . . . 399

60th Years Anniversary:INSTITUTE OF MATHEMATICS AND INFORMATICS –BULGARIAN ACADEMY OF SCIENCES . . . . . . . . . . . . . . . . . . . . . . . . 422

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Anniversary: TEN YEARS OF “FCAA” JOURNAL . . . . . . . . . . . . . . . . 1

M. Caputo, REPRINTED PAPER from the journal“Geophys. J. R. Astr. Soc.”, vol. 13, Issue 5 (1967), pp. 529-539:LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOSTFREQUENCY INDEPENDENT – II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3L.P. Castro, D. KapanadzePSEUDO-DIFFERENTIAL OPERATORS IN A WAVEDIFFRACTION PROBLEM WITH IMPEDANCE CONDITIONS . . . 15J.K. PrajapatINCLUSION PROPERTIES FOR CERTAIN CLASSES OFANALYTIC FUNCTIONS INVOLVING A FAMILY OFFRACTIONAL INTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . 27M. Benchohra, J. Henderson, S.K. Ntouyas, A. OuahabEXISTENCE RESULTS FOR FRACTIONAL FUNCTIONALDIFFERENTIAL INCLUSIONS WITH INFINITE DELAYAND APPLICATIONS TO CONTROL THEORY . . . . . . . . . . . . . . . . . . . 35Yu. LuchkoALGORITHMS FOR EVALUATION OF THE WRIGHTFUNCTION FOR THE REAL ARGUMENTS’ VALUES . . . . . . . . . . . . . 57A.D. Gadjiev, V.S. GuliyevTHE STEIN-WEISS TYPE INEQUALITY FOR FRACTIONALINTEGRALS, ASSOCIATED WITH THE LAPLACE-BESSELDIFFERENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77N.M. Fonseca Ferreira, F.B. Duarte, M.F.M. Lima,M.G. Marcos, J.A. Tenreiro MachadoAPPLICATION OF FRACTIONAL CALCULUS IN THE DYNAMICALANALYSIS AND CONTROL OF MECHANICAL MANIPULATORS.. 91

Meetings: ”Meetings in 2008” and ”FDA’2008”, Fractional Differen-tiation and its Applications, Ankara (Turkey), 5-7 Nov. 2008 . . . 114-116Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117-118

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Anniversary: TEN YEARS OF “FCAA” JOURNAL . . . . . . . . . . . . . . . . 1

M. Caputo, REPRINTED PAPER from the journal“Geophys. J. R. Astr. Soc.”, vol. 13, Issue 5 (1967), pp. 529-539:LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOSTFREQUENCY INDEPENDENT – II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3L.P. Castro, D. KapanadzePSEUDO-DIFFERENTIAL OPERATORS IN A WAVEDIFFRACTION PROBLEM WITH IMPEDANCE CONDITIONS . . . 15J.K. PrajapatINCLUSION PROPERTIES FOR CERTAIN CLASSES OFANALYTIC FUNCTIONS INVOLVING A FAMILY OFFRACTIONAL INTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . 27M. Benchohra, J. Henderson, S.K. Ntouyas, A. OuahabEXISTENCE RESULTS FOR FRACTIONAL FUNCTIONALDIFFERENTIAL INCLUSIONS WITH INFINITE DELAYAND APPLICATIONS TO CONTROL THEORY . . . . . . . . . . . . . . . . . . . 35Yu. LuchkoALGORITHMS FOR EVALUATION OF THE WRIGHTFUNCTION FOR THE REAL ARGUMENTS’ VALUES . . . . . . . . . . . . . 57A.D. Gadjiev, V.S. GuliyevTHE STEIN-WEISS TYPE INEQUALITY FOR FRACTIONALINTEGRALS, ASSOCIATED WITH THE LAPLACE-BESSELDIFFERENTIAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77N.M. Fonseca Ferreira, F.B. Duarte, M.F.M. Lima,M.G. Marcos, J.A. Tenreiro MachadoAPPLICATION OF FRACTIONAL CALCULUS IN THE DYNAMICALANALYSIS AND CONTROL OF MECHANICAL MANIPULATORS.. 91

Meetings: ”Meetings in 2008” and ”FDA’2008”, Fractional Differen-tiation and its Applications, Ankara (Turkey), 5-7 Nov. 2008 . . . 114-116Addresses of the EB Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117-118

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Anniversary: 70th ANNIVERSARY of Prof. Shyam L. Kalla: . . . . 119

R.K. Yadav, S.D. Purohit, S.L. KallaON GENERALIZED WEYL FRACTIONAL q-INTEGRALOPERATOR INVOLVING GENERALIZED BASICHYPERGEOMETRIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129B.T. Krishna, K.V.V.S. ReddyDESIGN OF FRACTIONAL ORDER DIGITAL DIFFERENTIATORSAND INTEGRATORS USING INDIRECT DISCRETIZATION . . . . 143Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Thanh HongGENERALIZED CONVOLUTION TRANSFORMSAND TOEPLITZ PLUS HANKEL INTEGRAL EQUATIONS . . . . . . 153N.A. Virchenko, O.V. RumiantsevaON THE GENERALIZED ASSOCIATEDLEGENDRE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175M. SharmaFRACTIONAL INTEGRATION AND FRACTIONALDIFFERENTIATION OF THE M-SERIES . . . . . . . . . . . . . . . . . . . . . . . . . 187V. Daftardar-Gejji, S. BhalekarSOLVING FRACTIONAL DIFFUSION-WAVE EQUATIONSUSING A NEW ITERATIVE METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . 193V. KiryakovaA BRIEF STORY ABOUT THE OPERATORS OFTHE GENERALIZED FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . 203Report on: ”The Wolfram Functions Site”, functions.wolfram.com” 186Announce for: Symposium on ”Fractional Calculus andApplications” at ”NSC’08”, Porto, July 2008 . . . . . . . . . . . . . . . . . . . . . . . 192Report on: ”AMS 2008 Spring Southeastern Meeting:Baton Rouge, LA, March 28-30, 2008” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221Announce for: ”Fourth Conference on Numerical Analysisand Applications, June 16-20, 2008, Lozenetz, Bulgaria” . . . . . . . . . . . . 225

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Anniversaries:85th ANNIVERSARY of Prof. Blagoj S. Popov . . . . . . . . . . . . . . . . . . . . . 22780th ANNIVERSARY of Prof. Paul L. Butzer . . . . . . . . . . . . . . . . . . . . . . 23075th ANNIVERSARY of Prof. Gary F. Roach . . . . . . . . . . . . . . . . . . . . . . 234I.S. Jesus, J.A. Tenreiro MachadoAN EVOLUTIONARY APPROACH FOR THE SYNTHESISOF FRACTIONAL POTENTIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237M. AssalGENERALIZED WAVE EQUATIONS IN THE SETTINGOF BESSEL-KINGMAN HYPERGROUPS . . . . . . . . . . . . . . . . . . . . . . . . . 249K. DiethelmON THE SEPARATION OF SOLUTIONSOF FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . 259H. Rafeiro, S. SamkoAPPROXIMATIVE METHOD FOR THE INVERSIONOF THE RIESZ POTENTIAL OPERATORIN VARIABLE LEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269K.M. Furati, M. KiraneNECESSARY CONDITIONS FOR THE EXISTENCE OFGLOBAL SOLUTIONS TO SYSTEMS OFFRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . 281V. KiryakovaTRANSMUTATION METHOD FOR SOLVINGHYPER-BESSEL DIFFERENTIAL EQUATIONS BASED ONTHE POISSON-DIMOVSKI TRANSFORMATION . . . . . . . . . . . . . . . . . 299

F. Merrikh-Bayat, M. Karimi-GhartemaniSOME PROPERTIES OF THREE-TERMFRACTIONAL ORDER SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317Y.Z. PovstenkoSIGNALING PROBLEM FOR TIME-FRACTIONALDIFFUSION-WAVE EQUATION IN A HALF-PLANE . . . . . . . . . . . . . 329T. KaczorekREALIZATION PROBLEM FOR POSITIVE FRACTIONALHYBRID 2D LINEAR SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

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Anniversary:60th ANNIVERSARY of Prof. Anatoly Kilbas . . . . . . . . . . . . . . . . . . . . . . 369S. SamkoANATOLY KILBAS’s 60th BIRTHDAY: CONGRATULATION . . . . 370S. RogozinPERSONAL LIFE OF A SCIENTIST:TO 60th BIRTHDAY OF PROFESSOR ANATOLY KILBAS . . . . . . . 373List of the main publicationsof Professor Anatoly Kilbas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378L. Ephremidze, V. Kokilashvili, S. SamkoFRACTIONAL, MAXIMAL AND SINGULAR OPERATORSIN VARIABLE EXPONENT LORENTZ SPACES . . . . . . . . . . . . . . . . . . 407A.N. KarapetyantsON FUNCTIONS ARISING AS POTENTIALSWITH OSCILLATING SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421L. Rodrıguez-Germa, J.J. Trujillo,L. Vazquez, M. Pilar VelascoFRACTIONAL CALCULUS FRAMEWORK TO AVOIDSINGULARITIES OF DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . 431F. Mainardi, G. PagniniMELLIN-BARNES INTEGRALS FOR STABLEDISTRIBUTIONS AND THEIR CONVOLUTIONS . . . . . . . . . . . . . . . . 443Yu.F. Luchko, H. Matrınez, J.J. TrujilloFRACTIONAL FOURIER TRANSFORMAND SOME OF ITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457A.A. Kilbas, A. KattuveettilREPRESENTATIONS OF DIRICHLET AVERAGES OFGENERALIZED MITTAG-LEFFLER FUNCTION VIAFRACTIONAL INTEGRALS AND SPECIAL FUNCTIONS . . . . . . . 471

New Book: by Yury A. Brychkov,“Handbook of Special Functions: Derivatives, Integrals,Series and Other Formulas”, CRC Press . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

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K. Haouam, M. SfaxiNONEXISTENCE RESULTS OF SOLUTIONS OF SEMILINEARDIFFERENTIAL INEQUALITIES WITH TEMPERALFRACTIONAL DERIVATIVE ON THE HEINSENBERG GROUP . . . 1E. Ait Dads, M. Benchohra, S. HamaniIMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONSINVOLVING THE CAPUTO FRACTIONAL DERIVATIVE . . . . . . . . . 15E.V. GuliyevON LIMITING CASE OF THE STEIN-WEISS TYPEINEQUALITY FOR THE B-RIESZ POTENTIALS . . . . . . . . . . . . . . . . . . 39F. Cipriano, H. Ouerdiane, R. Vilela MendesSTOCHASTIC SOLUTION OF A KPP-TYPE NONLINEARFRACTIONAL DIFFERENTIAL EQUATION . . . . . . . . . . . . . . . . . . . . . . . 47M.I. Gil’BOUNDS FOR FRACTIONAL POWERS OF OPERATORS IN AHILBERT SPACE & CONSTANTS IN MOMENT INEQUALITIES... 57M.A. Darwish, J. HendersonEXISTENCE AND ASYMPTOTIC STABILITYOF SOLUTIONS OF A PERTURBED QUADRATICFRACTIONAL INTEGRAL EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71D. NemzerA NOTE ON MULTIPLIERSFOR INTEGRABLE BOEHMIANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Z. TomovskiON HANKEL TRANSFORM OF GENERALIZEDMATHIEU SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97R.K. SaxenaA REMARK ON A PAPER ON M -SERIES . . . . . . . . . . . . . . . . . . . . . . . . . 109

Meetings: International Russian-Abkhazian Symposium,Nalchik-Elbrus (Kabardino-Balkarian Republic), 17-22 May 2009 . . . . . 111

Meetings: Report on 3rd IFAC Workshop ”FDA’08”,Ankara (Turkey), 5-7 November 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

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O. Parasyuk ‡, N. VirchenkoBRIEF SURVEY OF THE MATHEMATICAL LEGACYOF ACADEMICIAN M. KRAVCHUK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

A.N. KochubeiFRACTIONAL DIFFERENTIAL EQUATIONS:α-ENTIRE SOLUTIONS,REGULAR AND IRREGULAR SINGULARITIES . . . . . . . . . . . . . . . . . 135

Z.S.I. MansourLINEAR SEQUENTIAL q-DIFFERENCE EQUATIONSOF FRACTIONAL ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

C.A. Roberts, W.E. OlmsteadBLOW-UP IN A SUBDIFFUSIVE MEDIUMOF INFINITE EXTENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Yong ZhouEXISTENCE AND UNIQUENESS OF SOLUTIONSFOR A SYSTEM OF FRACTIONALDIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

A.A. Kilbas, N.V. ZhukovskayaEULER-TYPE NON-HOMOGENEOUS DIFFERENTIALEQUATIONS WITH THREELIOUVILLE FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . 205

Meetings in 2009: Letter by J.A. Tenreiro Machado . . . . . . . . . . . . . . 235

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Seema S. NairPATHWAY FRACTIONAL INTEGRATION OPERATOR . . . . . . . . . 237B.T. Giang, N.M. TuanGENERALIZED CONVOLUTIONS FOR THE INTEGRALTRANSFORMS OF FOURIER TYPE AND APPLICATIONS . . . . . 253I. PetrasSTABILITY OF FRACTIONAL-ORDER SYSTEMSWITH RATIONAL ORDERS: A SURVEY . . . . . . . . . . . . . . . . . . . . . . . . . 269R. Hilfer, Y. Luchko, Z. TomovskiOPERATIONAL METHOD FOR THE SOLUTION OFFRACTIONAL DIFFERENTIAL EQUATIONS WITH GENERALIZEDRIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES . . . . . . . . . . . 299H. Mejjaoli, N. SraiebGABOR TRANSFORM IN QUANTUM CALCULUSAND APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319R.K. SaxenaIN MEMORIUM OF CHARLES FOX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

New Books: V. V. UchaikinMETHOD OF FRACTIONAL DERIVATIVES (In Russian) . . . . . . . . 345Announce: O. MarichevWOLFRAM ALPHA – Computational Knowledge Engine . . . . . . . . . . 348Meetings in 2009: M. Duarte Ortigueira, J.A. Tenreiro MachadoSymp. on Fractional Signals and Systems, Lisbon, 4-6 Nov. 2009 . . . 351Meetings in 2010: Changpin Li, YangQuan Chen, Wen ChenMini-Symp. ”Fractional Dynamics and Control” at 3rd Intern. Conf. onDynamics, Vibration and Control, Hangzhou, 12-14 May 2010 . . . . . . 353Meetings in 2010: S. Sivasundaram // ICNPAA 2010 World Congress,8th Intern. Conf. on Mathematical Problems in Engineering, Aerospaceand Sciences, Brazil, 30 June-3 July 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355Editorial Board Addresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

Contents FCAA, Vol. 12, No 4 (2009)

F. Nouri, S. Bouaziz, N. BettaibiON A PALEY-WIENER THEOREM AND A q-SAMPLINGFORMULA FOR THE q-DUNKL TRANSFORM . . . . . . . . . . . . . . . . . . 359M. Talebpour, Y.M. Roshan, S.MohseniDEVELOPING ROBUST FFOPID CONTROLLERS BASEDON FUZZY SET POINT WEIGHTING ALGORITHM . . . . . . . . . . . . . 373T.J. Connolly, J.A. ContrerasBOND GRAPH PRIMITIVES FOR MODELING SYSTEMSWITH FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . 391Yu. LuchkoBVPs FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSIONEQUATION OF DISTRIBUTED ORDER . . . . . . . . . . . . . . . . . . . . . . . . . . 409T. KopalianiON THE HARDY INEQUALITY ON Lp(.)(Rn) SPACES . . . . . . . . . . 423A. CerneaON THE EXISTENCE OF SOLUTIONS FOR FRACTIONAL DIFFE-RENTIAL INCLUSIONS WITH BOUNDARY CONDITIONS . . . . . . 433I.H. DimovskiTHE COMMUTANT OF RIEMANN-LIOUVILLE OPERATOROF FRACTIONAL INTEGRATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443M. Sharma, R. Jain (Short Note)A NOTE ON A GENERALIZED M-SERIESAS A SPECIAL FUNCTION OF FRACTIONAL CALCULUS . . . . . 449U.K. Saha, K.K. Arora, A.K. Arora (Short Note)ON THE RELATIONSHIPS OF THE R-FUNCTIONOF LORENZO AND HARTLEY WITH OTHER SFs of FC . . . . . . . . 453ANNIVERSARIES: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459Prof. Yury A. Brychkov, 65th Anniversary . . . . . . . . . . . . . . . . . . . . . . . . . . 460Prof. Mourad E.H. Ismail, 65th Anniversary . . . . . . . . . . . . . . . . . . . . . . . . 466Prof. Ivan H. Dimovski, 75th Anniversary . . . . . . . . . . . . . . . . . . . . . . . . . . 474MEETINGS in 2010, Announces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477– Report on 5th AMADE-2009: Minsk, Belarus, Sept. 2009;by Gaishun, Dubatovskaya, Kilbas, Rogosin, Zhuravkov . . . . . . . . . . . . . 477– AUS-ICMS’10: American Univ. Sharjah, UAE, March 2010 . . . . 479– Conf. to Acad. M. Kravchuk: Kiev, Ukraine, May 2010 . . . . . . 481– Constr. Function Theory’10: Sozopol, Bulgaria, June 2010 . . . 482– Geometric Function Theory and Applications’2010: Sofia,Bulgaria, August 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483– Fract. Diff. and Applications’10: Badajoz, Spain, Oct. 2010 . . 484


A. Gil, S. SamkoON A HYPERSINGULAR EQUATION OF A PROBLEM,FOR A CRACK IN ELASTIC MEDIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1A.L. Soubhia, R.F. Camargo, E.C. de Oliveira, J. Vaz Jr.THEOREM FOR SERIES IN THREE-PARAMETERMITTAG-LEFFLER FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9M.N. StojanovicWELL-POSEDNESS OF DIFFUSION-WAVE PROBLEMWITH ARBITRARY FINITE NUMBER OF TIMEFRACTIONAL DERIVATIVES IN SOBOLEV SPACES Hs . . . . . . . . . 21E. Ournycheva, B. RubinON Y. NIEVERGELT’S INVERSION FORMULAFOR THE RADON TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Y. Nikolova, L. BoyadjievINTEGRAL TRANSFORMS METHOD TO SOLVEA TIME-SPACE FRACTIONAL DIFFUSION EQUATION . . . . . . . . . . 57A.A. Kilbas, O.A. RepinAN ANALOG OF THE TRICOMI PROBLEMFOR A MIXED TYPE EQUATIONWITH A PARTIAL FRACTIONAL DERIVATIVE . . . . . . . . . . . . . . . . . . 69P. RusevHERMITE POLYNOMIALS AND THEZERO-DISTRIBUTION OF RIEMANN’S ζ-FUNCTION . . . . . . . . . . . . 85

MEETINGS in 2010, Announces:2nd ”AMiTaNS” Conf., Sozopol, Bulgaria, June 21-16 . . . . . . . . . . . . . . . . 68”HART”, Lisbon, Portugal, June 21-25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96”GFTA’10”, Sofia, Bulgaria, August 27-31 . . . . . . . . . . . . . . . . . . . . . . . . . . . 97”FDA’10”, Badajoz, Spain, October 18-20 . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

NEW BOOK: R. Caponetto, G. Dongola, L. Fortuna, I. Petras,Fractional Order Systems (Modeling and Control Applications) . . 101

Contents of Volumes 11 and 12 (2008, 2009) . . . . . . . . . . . . . . 103-110


Anniversary:75th ANNIVERSARY of Prof. A.M. MATHAI . . . . . . . . . . . . . . . . . . . . . . 111

A.M. MathaiSOME PROPERTIES OF MITTAG-LEFFLER FUNCTIONSAND MATRIX-VARIATE ANALOGUES:A STATISTICAL PERSPECTIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113H. Haubold, D. Kumar, S.S. Nair, D.P. JosephSPECIAL FUNCTIONS AND PATHWAYSFOR PROBLEMS IN ASTROPHYSICS:AN ESSAY IN HONOR OF A.M. MATHAI . . . . . . . . . . . . . . . . . . . . . . . . 133A.A. Kilbas †, N. SebastianFRACTIONAL INTEGRATION OF THE PRODUCTOF BESSEL FUNCTIONS OF THE FIRST KIND . . . . . . . . . . . . . . . . . 159R.K. Saxena, R. Saxena, S.L. KallaSOLUTION OF SPACE-TIME FRACTIONALSCHRODINGER EQUATION OCCURRINGIN QUANTUM MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177M. Garg, P. ManoharNUMERICAL SOLUTION OF FRACTIONALDIFFUSION-WAVE EQUATION WITHTWO SPACE VARIABLES BY MATRIX METHOD . . . . . . . . . . . . . . . 191

Meetings: ICMS 2011 (Jan. 3–5, 2011, Kerala, India)“International Conference on Mathematical Sciencesin Honour of Prof. A.M. Mathai” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

New Book: by A.M. Mathai, H.J. Haubold,“Special Functions for Applied Scientists”, Springer, 2008 . . . . . . . . . . . 213New Book: by A.M. Mathai, R.K. Saxena, H.J. Haubold,“The H-Function”, Springer, 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216New Book: by F. Mainardi,“Fractional Calculus and Waves in Linear Viscoleasticity”,World Sci. & Imperial College Press, 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . 219

In Memoriam: Anatoly Alexandrovich Kilbas . . . . . . . . . . . . . . . . . . . . . 221


S. Abbas, M. BenchohraIMPULSIVE PARTIAL HYPERBOLIC FUNCTIONALDIFFERENTIAL EQUATIONS OF FRACTIONAL ORDERWITH STATE-DEPENDENT DELAY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225T. Mamatov, S. SamkoMIXED FRACTIONAL INTEGRATION OPERATORS IN MIXEDWEIGHTED HOLDER SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Ch. Chettaoui, Kh. TrimecheBOCHNER-HECKE THEOREMS FOR THE WEINSTEINTRANSFORM AND APPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261A. Anguraj, P. KarthikeyanANTI-PERIODIC BOUNDARY VALUE PROBLEMFOR IMPULSIVE FRACTIONALINTEGRO DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 281M.S. Samuel, A. ThomasON FRACTIONAL HELMHOLTZ EQUATIONS . . . . . . . . . . . . . . . . . . . 295D. Kumar, A. Kilbas ‡

FRACTIONAL CALCULUS OF P - TRANSFORMS . . . . . . . . . . . . . . 309J.A. Tenreiro Machado, V. Kiryakova, F. MainardiA POSTER ABOUT THE RECENT HISTORYOF FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

New Book: by K. Diethelm, THE ANALYSIS OFFRACTIONAL DIFFERENTIAL EQUATIONS, Springer 2010 . . . . . 335Anniversaries:RUDOLF GORENFLO’s 80th BIRTHDAY ANNIVERSARY . . . . . . . 341HARI M. SRIVASTAVA’s 70th BIRTHDAY ANNIVERSARY . . . . . . 342Corrigendum: to paper by M.K. Furati and M. Kirane,in FCAA, Vol. 11, Number 3 (2008), pp. 281-298 . . . . . . . . . . . . . . . . . . . 343Symposium’s Announce: The Fifth Symposium onFractional Derivatives and Their Applications (FDTA’11),August 29 – 31, 2011, Washington D.C., USA . . . . . . . . . . . . . . . . . . . . . . . 344

ISSN 1311-0454 FCAA, Vol. 13, No 4 (2010)

CONTENTS

Guest-Editors: Virginia Kiryakova and S. OwaSpecial Issue: ”GFTA’2010” - Sofia, PART A

Dedicated to 70th Anniversary of Prof. H.M. Srivastava

Editorial: PROF. H.M. SRIVASTAVA’S 70th BIRTHDAY . . . . . . . . . 346Editorial: International Symposium GFTA’2010: “GEOMETRICFUNCTION THEORY AND APPLICATIONS’2010” . . . . . . . . . . . . . . . 353A. Alb LupasCERTAIN DIFFERENTIAL SUBORDINATIONS USING GENERALI-ZED SALAGEAN OPERATOR & RUSCHEWEYH OPERATOR . . 355M. Aydogan, Y. PolatogluAPPLICATION OF SUBORDINATION PRINCIPLE TOLOG-HARMONIC α-SPIRALLIKE MAPPINGS . . . . . . . . . . . . . . . . . . . 361T. Hayami, S. OwaCOEFFICIENT ESTIMATES FOR ANALYTIC FUNCTIONSCONCERNED WITH HANKEL DETERMINANT . . . . . . . . . . . . . . . . . 367T.N. Shanmugam , J. Lourthu MaryFEKETE-SZEGO INEQUALITY FORUNIVERSALLY PRESTARLIKE FUNCTIONS . . . . . . . . . . . . . . . . . . . . 385J. Nishiwaki, S. OwaAN APPLICATION OF CONVOLUTION INTEGRAL . . . . . . . . . . . . . 395J. Paneva-KonovskaSERIES IN MITTAG-LEFFLER FUNCTIONS:INEQUALITIES AND CONVERGENT THEOREMS . . . . . . . . . . . . . . 403D. PashkoulevaSOME NOTES ABOUT A CLASS OF UNIVALENTFUNCTIONS WITH NEGATIVE COEFFICIENTS . . . . . . . . . . . . . . . . 415Dj. Takaci, A. TakaciON THE OPERATIONAL SOLUTION OF A SYSTEM OFFRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . 423Y.Ts. TsankovEXPLICIT SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROB-LEMS, CONTAINING BITSADZE-SAMARSKII CONSTRAINTS... 435J.A. Tenreiro Machado, V. Kiryakova, F. MainardiA POSTER ABOUT THE OLD HISTORYOF FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

Conference Announces 2011: IDOTA, FDTA, AMADE, Others 455Information on the new FCAA status . . . . . . . . . . . . . . . . . . . . . . . . 463

ISSN 1311-0454 FCAA, Vol. 13, No 5 (2010)

CONTENTS

Guest-Editors: Virginia Kiryakova and S. OwaSpecial Issue: ”GFTA’2010” - Sofia, PART B

Editorial: International Symposium GFTA’2010: . . . . . . . . . . . . . . . . . . 465

B. DarabyINVESTIGATION OF A STOLARSKY TYPE INEQUALITYFOR INTEGRALS IN PSEUDO-ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . 467M. Darus, R.W. IbrahimA NOTE ON UNIVALENT FUNCTIONS WITHFINITELY MANY COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475H. Esra Ozkan, Y. Polatoglu, A. SenAPPLICATIONS OF SUBORDINATION PRINCIPLE TOLOG-HARMONIC MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487K. FujitaON THE QUOTIENT FUNCTION EMPLOYED INTHE BLIND SOURCE SEPARATION PROBLEM . . . . . . . . . . . . . . . . . 495Jianhua GongHILBERT-SMITH CONJECTURE FORK−QUASICONFORMAL GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507Sh. NajafzadehAPPLICATION OF SALAGEAN AND RUSCHEWEYHOPERATORS ON UNIVALENT HOLOMORPHICFUNCTIONS WITH FINITELY MANY COEFFICIENTS . . . . . . . . . 517G.I. OrosAN APPLICATION OF THE SUBORDINATION CHAINS . . . . . . . . 521Gh. Oros, G.I. OrosON A CONVEXITY PRESERVING INTEGRAL OPERATOR . . . . . 531Y. PolatogluSOME GROWTH AND DISTORTION THEOREMS FOR CLOSE-TO-CONVEX HARMONIC FUNCTIONS IN THE UNIT DISC . . . . . . . . 537E. Yavuz DumanSOME DISTORTION THEOREMS FORSTARLIKE HARMONIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545N. Uyanik, S. OwaNOTE ON RADIUS PROBLEMS FOR CERTAIN CLASSOF ANALYTIC FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553

Editorial: GHEORGHE OROS’ 60th ANNIVERSARY . . . . . . . . . . . . 561Editorial: YASAR POLATOGLU’S 60th ANNIVERSARY . . . . . . . . 563

ISSN 1311-0454, eISSN 1314-2224 FCAA, Vol. 14, No 1 (2011)

CONTENTS

Guest-Editors: Virginia Kiryakova, Yury Luchko,Francesco Mainardi, Blas Vinagre, Igor Podlubny, YangQuan ChenSpecial Issue: Dedicated to 80th Anniversary of Prof. R. Gorenflo

Editorial: FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Yu. Luchko, F. Mainardi, S. RogosinPROFESSOR RUDOLF GORENFLOAND HIS CONTRIBUTION TO FRACTIONAL CALCULUS . . . . . . . 3S. SamkoON A 3d-HYPERSINGULAR EQUATIONOF A PROBLEM FOR A CRACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Vu Kim TuanINVERSE PROBLEM FOR FRACTIONALDIFFUSION EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31M. Hahn, S. UmarovFRACTIONAL FOKKER-PLANCK-KOLMOGOROV TYPEEQUATIONS AND THEIR ASSOCIATEDSTOCHASTIC DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . 56G. PagniniNONLINEAR TIME-FRACTIONAL DIFFERENTIALEQUATIONS IN COMBUSTION SCIENCE . . . . . . . . . . . . . . . . . . . . . . . . 80T.M. Atanackovic, S. PilipovicHAMILTON’S PRINCIPLE WITH VARIABLEORDER FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Yu. LuchkoMAXIMUM PRINCIPLE AND ITS APPLICATIONFOR THE TIME-FRACTIONAL DIFFUSION EQUATIONS . . . . . . 110M. StojanovicFRACTIONAL DERIVATIVES IN SPACESOF GENERALIZED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125A.M. Mathai, H.J. HauboldMATRIX-VARIATE STATISTICAL DISTRIBUTIONSAND FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Conference: IDOTA-2011, June 30-July 2, 2011, Aveiro, Portugal(On the occasion of 70th birthday of Prof. S. Samko) . . . . . . . . . . . . . . 156Conference: FDTA-2011, August 29-31, 2011, Washington D.C., USA(5th Symp. on Fractional Derivatives and Their Applications) . . . . . . 158Conference: AMADE-2011, September 12-19, 2011, Minsk, Belarus(Dedicated to the memory of Prof. A.A. Kilbas) . . . . . . . . . . . . . . . . . . . 160


CONTENTS

Editorial: PRESS RELEASE:First Bulgarian journal published by Springer and Versita . . . . . . . . . . 163

D. Przeworska-RolewiczSHIFTS AND PERIODICITY IN ALGEBRAIC ANALYSIS . . . . . . . 164

C. Atkinson, A. OsseiranDISCRETE-SPACE TIME-FRACTIONAL PROCESSES . . . . . . . . . . 201

A. AbouelazTHE d-PLANE RADON TRANSFORMON THE TORUS T

n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

A. Obeidat, M. Gharaibeh, M. Al-Ali, A. RousanEVOLUTION OF A CURRENT IN A RESISTOR . . . . . . . . . . . . . . . . . 247

K.N. Khan, W. Lamb, A.C. McBrideFRACTIONAL CALCULUS OFPERIODIC DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

T. Morita, K. SatoMOLLIFICATION OF FRACTIONAL DERIVATIVESUSING RAPIDLY DECAYING HARMONIC WAVELET . . . . . . . . . . 284

M. KosticABSTRACT TIME-FRACTIONAL EQUATIONS:EXISTENCE AND GROWTH OF SOLUTIONS . . . . . . . . . . . . . . . . . . . 301

D. Babusci, G. Dattoli, D. SacchettiTHE LAMB-BATEMAN INTEGRAL EQUATIONAND THE FRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . 317

Conference: TMSF’2011, October 20-23, 2011, Sofia, Bulgaria(On the occasion of 80th anniversary of Prof. P. Rusev) . . . . . . . . . . . . 321


CONTENTS

Editorial:FCAA NEWS, BOOKS, MEETINGS, ANNIVERSARIES . . . . . . . . . . 323

L. Vazquez, J.J. Trujillo, M.P. VelascoFRACTIONAL HEAT EQUATION ANDTHE SECOND LAW OF THERMODYNAMICS . . . . . . . . . . . . . . . . . . . 334

H. Rafeiro, M. YakhshiboevTHE CHEN-MARCHAUD FRACTIONALINTEGRO-DIFFERENTIATION IN THE VARIABLEEXPONENT LEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

L. Diening, D. Cruz-Uribe, P. HastoTHE MAXIMAL OPERATOR ON WEIGHTEDVARIABLE LEBESGUE SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

J.P.N. BishwalMINIMUM CONTRAST ESTIMATION IN FRACTIONALORNSTEIN-UHLENBECK PROCESS:CONTINUOUS AND DISCRETE SAMPLING . . . . . . . . . . . . . . . . . . . . 375

J. KemppainenEXISTENCE AND UNIQUENESS OF THE SOLUTIONFOR A TIME-FRACTIONAL DIFFUSION EQUATION . . . . . . . . . . 411

Y. PovstenkoNON-AXISYMMETRIC SOLUTIONSTO TIME-FRACTIONAL DIFFUSION-WAVE EQUATIONIN AN INFINITE CYLINDER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

Z. Jiao, Y.Q. ChenSTABILITY ANALYSIS OF FRACTIONAL-ORDERSYSTEMS WITH DOUBLE NONCOMMENSURATEORDERS FOR MATRIX CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

N.J. Ford, J. Xiao, Y. YanA FINITE ELEMENT METHOD FOR TIME FRACTIONALPARTIAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 454

K. DiethelmAN EFFICIENT PARALLEL ALGORITHMFOR THE NUMERICAL SOLUTIONOF FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . 475


CONTENTS

Editorial:FCAA NEWS: MEETINGS, BOOKS, ANNIVERSARIES . . . . . . . . . . 491

P. Lanusse, J. SabatierPLC IMPLEMENTATION OF A CRONE CONTROLLER . . . . . . . . 505

A.B. Malinowska, D.F.M. TorresFRACTIONAL CALCULUS OF VARIATIONSFOR A COMBINED CAPUTO DERIVATIVE . . . . . . . . . . . . . . . . . . . . . 523

D. Idczak, R. KamockiON THE EXISTENCE AND UNIQUENESSAND FORMULA FOR THE SOLUTIONOF R-L FRACTIONAL CAUCHY PROBLEM IN Rn . . . . . . . . . . . . . 538

N.J. Ford, M.L. MorgadoFRACTIONAL BOUNDARY VALUE PROBLEMS:ANALYSIS AND NUMERICAL METHODS . . . . . . . . . . . . . . . . . . . . . . . 554

G. Baumann, F. StengerFRACTIONAL CALCULUS AND SINC METHODS . . . . . . . . . . . . . . 568

Z. Tomovski, T.K. PoganyINTEGRAL EXPRESSIONS FOR MATHIEU–TYPEPOWER SERIES AND FORTHE BUTZER–FLOCKE–HAUSS Ω–FUNCTION . . . . . . . . . . . . . . . . . 623

J. Tenreiro MachadoAND I SAY TO MYSELF:“WHAT A FRACTIONAL WORLD !” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635


CONTENTS

FCAA NEWS: MEETINGS AND BOOKS . . . . . . . . . . . . . . . . . . . . . . . . . . 1

J.R. Graef, L. Kong, B. YangPOSITIVE SOLUTIONS FOR A SEMIPOSITONEFRACTIONAL BOUNDARY VALUE PROBLEMWITH A FORCING TERM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Yu.S. LinchukCOMMUTANTS OF COMPOSITION OPERATORSINDUCED BY A PARABOLIC LINEAR FRACTIONALAUTOMORPHISMS OF THE UNIT DISK . . . . . . . . . . . . . . . . . . . . . . . . . 25

B. RubinON SOME INVERSION FORMULASFOR RIESZ POTENTIALS AND k-PLANE TRANSFORMS . . . . . . . 34

A. Aghajani, Y. Jalilian, J.J. TrujilloON THE EXISTENCE OF SOLUTIONS OFFRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS . . . . . . . . 44

B.J. West, D. WestFRACTIONAL DYNAMICS OF ALLOMETRY . . . . . . . . . . . . . . . . . . . . 70

Z. Jiao, Y. Q. ChenIMPULSE RESPONSE OF A GENERALIZEDFRACTIONAL SECOND ORDER FILTER . . . . . . . . . . . . . . . . . . . . . . . . 97

G. PagniniERDELYI–KOBER FRACTIONAL DIFFUSION . . . . . . . . . . . . . . . . . . . 117

K. Hu, N. Jacob, C. YuanON AN EQUATION BEING A FRACTIONAL DIFFERENTIALEQUATION WITH RESPECT TO TIME AND APSEUDO-DIFFERENTIAL EQUATION WITH RESPECTTO SPACE RELATED TO LEVY-TYPE PROCESSES . . . . . . . . . . . . 128

Yu. LuchkoINITIAL-BOUNDARY-VALUE PROBLEMSFOR THE ONE-DIMENSIONAL TIME-FRACTIONALDIFFUSION EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141


CONTENTS

FCAA NEWS, RELATED MEETINGS AND BOOKS . . . . . . . . . . . . . . . . . . 161S. Abbas, M. Benchohra, A.N. VityukON FRACTIONAL ORDER DERIVATIVES AND DARBOUXPROBLEM FOR IMPLICIT DIFFERENTIAL EQUATIONS . . . . . . . . . . . 168A. CerneaA NOTE ON THE EXISTENCE OF SOLUTIONS FOR SOME BOUNDARYVALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL INCLUSIONS 183J. KemppainenSOLVABILITY OF A DIRICHLET PROBLEM FOR A TIME FRACTIONALDIFFUSION-WAVE EQUATION IN LIPSCHITZ DOMAINS . . . . . . . . . . . 195C. AtkinsonMOVING BOUNDARY PROBLEMS FOR TIME FRACTIONALAND COMPOSITION DEPENDENT DIFFUSION . . . . . . . . . . . . . . . . . . . . 207S.R. Grace, R.P. Agarwal, P.J.Y. Wong, A. ZaferON OSCILLATION OF FRACTIONAL DIFFERENTIAL EQUATIONS . 222E. BazhlekovaEXISTENCE AND UNIQUENESS RESULTS FOR AFRACTIONAL EVOLUTION EQUATION IN HILBERT SPACE . . . . . . . 232G. Wang, D. Baleanu, L. ZhangMONOTONE ITERATIVE METHOD FOR A CLASS OFNONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . 244Y. PovstenkoNON-CENTRAL-SYMMETRIC SOLUTION TOTIME-FRACTIONAL DIFFUSION-WAVE EQUATION IN ASPHERE UNDER DIRICHLET BOUNDARY CONDITION . . . . . . . . . . . . 253K.M. Shinaliyev, B.Kh. Turmetov, S.R. UmarovA FRACTIONAL OPERATOR ALGORITHM METHODFOR CONSTRUCTION OF SOLUTIONS OF FRACTIONALORDER DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267I. PetrasTUNING AND IMPLEMENTATION METHODS FORFRACTIONAL-ORDER CONTROLLERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282K. DiethelmTHE MEAN VALUE THEOREMS AND A NAGUMO-TYPE UNIQUENESSTHEOREM FOR CAPUTO’S FRACTIONAL CALCULUS . . . . . . . . . . . . . 304E. Scalas, N. VilesON THE CONVERGENCE OF QUADRATIC VARIATIONFOR COMPOUND FRACTIONAL POISSON PROCESSES . . . . . . . . . . . . 314R. HerrmannCOVARIANT FRACTIONAL EXTENSION OF THE MODIFIEDLAPLACE-OPERATOR USED IN 3D-SHAPE RECOVERY . . . . . . . . . . . . 332


CONTENTS

Editorial: FCAA RELATED MEETINGS, BOOKS, IN MEMORIAM(FCAA - Volume 15 - No 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

D. Bouagada, P. Van DoorenSTATE SPACE SOLUTION OF IMPLICIT FRACTIONALCONTINUOUS TIME SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356B. Ahmad, S. NtouyasFRACTIONAL DIFFERENTIAL INCLUSIONS WITHFRACTIONAL SEPARATED BOUNDARY CONDITIONS . . . . . . . . . . . . . 362C.P. Li, F.H. Zeng, F. LiuSPECTRAL APPROXIMATIONS TO THE FRACTIONALINTEGRAL AND DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383A.B. Malinowska, D.F.M. TorresTOWARDS A COMBINED FRACTIONAL MECHANICSAND QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407D. Idczak, S. WalczakA FRACTIONAL IMBEDDING THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . 418T. Sandev, R. Metzler, Z. TomovskiVELOCITY AND DISPLACEMENT CORRELATIONFUNCTIONS FOR FRACTIONALGENERALIZED LANGEVIN EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 426B. Ahmad, J.J. NietoANTI-PERIODIC FRACTIONAL BOUNDARY VALUEPROBLEMS WITH NONLINEAR TERM DEPENDINGON LOWER ORDER DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451D. Bolster, M. M. Meerschaert, A. SikorskiiPRODUCT RULE FOR VECTOR FRACTIONALDERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463C. Zeng, Y.Q. Chen, Q. YangTHE FBM-DRIVEN ORNSTEIN-UHLENBECK PROCESS:PROBABILITY DENSITY FUNCTION AND ANOMALOUS DIFFUSION 479N.X. Thao, V.K. Tuan, N.T. HongA FOURIER GENERALIZED CONVOLUTION TRANSFORMAND APPLICATIONS TO INTEGRAL EQUATIONS . . . . . . . . . . . . . . . . . 493J.R. Graef, L. Kong, Q. Kong, M. WangUNIQUENESS OF POSITIVE SOLUTIONS OF FRACTIONALBOUNDARY VALUE PROBLEMS WITHNON-HOMOGENEOUS INTEGRAL BOUNDARY CONDITIONS . . . . . . 509


CONTENTS

Editorial: FCAA RELATED MEETINGS, BOOKS, IN MEMORIAM(FCAA - Volume 15 - No 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529B. DudaFRACTIONAL CALCULUS FOR POWER FUNCTIONSAND EIGENVALUES OF THE FRACTIONAL LAPLACIAN . . . . . . . . . . 536D. Rostamy, K. KarimiBERNSTEIN POLYNOMIALS FOR SOLVINGFRACTIONAL HEAT- AND WAVE-LIKE EQUATIONS . . . . . . . . . . . . . . . 556R.P. Agarwal, S. Arshad, D. O’Regan, V. LupulescuFUZZY FRACTIONAL INTEGRAL EQUATIONSUNDER COMPACTNESS TYPE CONDITION . . . . . . . . . . . . . . . . . . . . . . . . 572Li Kexue, Peng Jigen, Gao JinghuaiEXISTENCE RESULTS FOR SEMILINEAR FRACTIONALDIFFERENTIAL EQUATIONS VIA KURATOWSKIMEASURE OF NONCOMPACTNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591R.A.C. FerreiraA UNIQUENESS RESULT FOR A FRACTIONALDIFFERENTIAL EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611P.A. WilliamsFRACTIONAL CALCULUS ON TIME SCALESWITH TAYLOR’S THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616C.-G. Li, M. Kostic, M. Li, S. PiskarevON A CLASS OF TIME-FRACTIONALDIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639N.H. Sweilam, M.M. Khader, H.M. AlmarwmNUMERICAL STUDIES FOR THE VARIABLE-ORDERNONLINEAR FRACTIONAL WAVE EQUATION . . . . . . . . . . . . . . . . . . . . . 669C.D. Dhaigude, V.R. NikamSOLUTION OF FRACTIONAL PARTIAL DIFFERENTIALEQUATIONS USING ITERATIVE METHOD . . . . . . . . . . . . . . . . . . . . . . . . . 684O. AgrawalSOME GENERALIZED FRACTIONAL CALCULUS OPERATORSAND THEIR APPLICATIONS IN INTEGRAL EQUATIONS . . . . . . . . . . . 700F. MainardiAN HISTORICAL PERSPECTIVE ON FRACTIONALCALCULUS IN LINEAR VISCOELASTICITY . . . . . . . . . . . . . . . . . . . . . . . . 712R.R. Nigmatulllin, D. BaleanuTHE DERIVATION OF THE GENERALIZED FUNCTIONALEQUATIONS DESCRIBING SELF-SIMILAR PROCESSES . . . . . . . . . . . . . 718


CONTENTS

SPECIAL ISSUE:

“Fractional Differentiation and Its Applications’ 2012”(Papers selected from the 5th Symposium FDA’ 2012,

Hohai University, China)

Guest Editors: Virginia Kiryakova, Wen Chen,Mark M. Meerschaert, Igor Podlubny

Editorial: FCAA RELATED MEETINGS AND NEWS(FCAA–Volume 16–1–2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

F. Liu, M.M. Meerschaert, R.J. McGough, P. Zhuang, Q. LiuNUMERICAL METHODS FOR SOLVING THE MULTI-TERMTIME-FRACTIONAL WAVE-DIFFUSION EQUATION . . . . . . . . . . . . . . . . . 9

S. P. Nasholm, S. HolmON A FRACTIONAL ZENER ELASTIC WAVE EQUATION . . . . . . . . . . . 26

J. Liang, Z. Liu, X. WangSOLVABILITY FOR A COUPLE SYSTEM OF NONLINEARFRACTIONAL DIFFERENTIAL EQUATIONS IN A BANACH SPACE . . 51

T. Odzijewicz, A.B. Malinowska, D.F.M. TorresGREEN’S THEOREM FOR GENERALIZEDFRACTIONAL DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

W. Chen, J.J. Zhang, J.Y. ZhangA VARIABLE-ORDER TIME-FRACTIONAL DERIVATIVE MODEL FORCHLORIDE IONS SUB-DIFFUSION IN CONCRETE STRUCTURES . . . 76

R. Caponetto, G. Maione, A. Pisano, M.R. Rapaic, E. UsaiANALYSIS AND SHAPING OF THE SELF-SUSTAINED OSCILLATIONSIN RELAY CONTROLLED FRACTIONAL-ORDER SYSTEMS . . . . . . . . . 93

H. Jafari, H. Tajadodi, D. BaleanuA MODIFIED VARIATIONAL ITERATION METHODFOR SOLVING FRACTIONAL RICCATI DIFFERENTIALEQUATION BY ADOMIAN POLYNOMIALS . . . . . . . . . . . . . . . . . . . . . . . . . 109

(Continued on back cover page)

CONTENTS, continued:

P. Guo, C.B. Zeng, C.P. Li, Y.Q. ChenNUMERICS FOR THE FRACTIONAL LANGEVIN EQUATIONDRIVEN BY THE FRACTIONAL BROWNIAN MOTION . . . . . . . . . . . . . 123

J.G. Lu, Y.Q. ChenSTABILITY AND STABILIZATION OF FRACTIONAL-ORDERLINEAR SYSTEMS WITH CONVEX POLYTOPIC UNCERTAINTIES . 142

A.A. Khamzin, R.R. Nigmatullin, I.I. Popov, B.A. MurzalievMICROSCOPIC MODEL OF DIELECTRICα-RELAXATION IN DISORDERED MEDIA . . . . . . . . . . . . . . . . . . . . . . . . . . 158

K.M. FuratiBOUNDS ON THE SOLUTION OF A CAUCHY-TYPEPROBLEM INVOLVING A WEIGHTEDSEQUENTIAL FRACTIONAL DERIVATIVE . . . . . . . . . . . . . . . . . . . . . . . . . 171

L.C. Chen, F. Hu, W.Q. ZhuSTOCHASTIC DYNAMICS AND FRACTIONAL OPTIMALCONTROL OF QUASI INTEGRABLE HAMILTONIANSYSTEMS WITH FRACTIONAL DERIVATIVE DAMPING . . . . . . . . . . . 189

B. Guo, Z. HuoWELL-POSEDNESS FOR THE NONLINEAR FRACTIONALSCHRODINGER EQUATION AND INVISCID LIMITBEHAVIOR OF SOLUTION FORTHE FRACTIONAL GINZBURG-LANDAU EQUATION . . . . . . . . . . . . . . . 226

M. Klimek, M. LupaREFLECTION SYMMETRIC FORMULATION OF GENERALIZEDFRACTIONAL VARIATIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . 243

P. Straka, M.M. Meerschaert, R.J. McGough, Y. ZhouFRACTIONAL WAVE EQUATIONS WITH ATTENUATION . . . . . . . . . . 262

R. Malti, M. ThomassinDIFFERENTIATION SIMILARITIES IN FRACTIONALPSEUDO-STATE SPACE REPRESENTATIONSAND THE SUBSPACE-BASED METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . 273


CONTENTS

SPECIAL ISSUE:

Dedicated to 70th Anniversary of Prof. Francesco Mainardi

Guest Editors:Rudolf Gorenflo, Yuri Luchko, Virginia Kiryakova

Editorial: FCAA RELATED NEWS, EVENTS AND BOOKS(FCAA–Volume 16–2–2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

R. Gorenflo, Yu. Luchko, and M. StojanovicFUNDAMENTAL SOLUTION OF A DISTRIBUTEDORDER TIME-FRACTIONAL DIFFUSION-WAVEEQUATION AS PROBABILITY DENSITY . . . . . . . . . . . . . . . . . . . . . . . 297

C. Zeng, Y.Q. Chen, Q. YangALMOST SURE AND MOMENT STABILITY PROPERTIESOF FRACTIONAL ORDER BLACK-SCHOLES MODEL . . . . . . . . . 317

D. Fulger, E. Scalas, G. GermanoRANDOM NUMBERS FROM THE TAILSOF PROBABILITY DISTRIBUTIONS USINGTHE TRANSFORMATION METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

Y. PovstenkoTIME-FRACTIONAL HEAT CONDUCTIONIN AN INFINITE MEDIUM WITH A SPHERICAL HOLEUNDER ROBIN BOUNDARY CONDITION . . . . . . . . . . . . . . . . . . . . . . . 354

S. SamkoA NOTE ON RIESZ FRACTIONAL INTEGRALSIN THE LIMITING CASE α(x)p(x) ≡ n . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

A.A. Kilbas, A.A. Koroleva, S.V. RogosinMULTI-PARAMETRIC MITTAG-LEFFLER FUNCTIONSAND THEIR EXTENSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

Yu. Luchko, V. KiryakovaTHE MELLIN INTEGRAL TRANSFORMIN FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405



P. RusevREPRESENTATION OF HOLOMORPHIC FUNCTIONSBY SCHLOMILCH’S SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

G. PagniniTHE M-WRIGHT FUNCTIONAS A GENERALIZATION OF THE GAUSSIAN DENSITYFOR FRACTIONAL DIFFUSION PROCESSES . . . . . . . . . . . . . . . . . . . 436

N.J. Ford, M.M. Rodrigues, N. VieiraA NUMERICAL METHOD FOR THE FRACTIONALSCHRODINGER TYPE EQUATIONOF SPATIAL DIMENSION TWO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454

A.M. Mathai, H.J. HauboldFRACTIONAL OPERATORS IN THE MATRIXVARIATE CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

J. Tenreiro Machado, A.M. Galhano, J.J. TrujilloSCIENCE METRICS ON FRACTIONAL CALCULUSDEVELOPMENT SINCE 1966 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

I. PodlubnyWHAT EULER COULD FURTHER WRITE, ORTHE UNNOTICED “BIG BANG”OF THE FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501


CONTENTS


J. MunkhammarCHAOS IN A FRACTIONAL ORDER LOGISTIC MAP . . . . . . . . . . 511

R. Abi Zeid Daou, X. Moreau, C. FrancisEFFECTS OF THE TEMPERATURE VARIATION ONTHE BEHAVIOR OF THE FIRST ORDER CRONESYSTEM REALIZED IN THE ELECTRICAL DOMAIN . . . . . . . . . . 520

P.D. Phung, L.X. TruongON A FRACTIONAL DIFFERENTIAL INCLUSIONWITH INTEGRAL BOUNDARY CONDITIONSIN BANACH SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

W. Okrasinski, ÃL. PÃlociniczakA NOTE ON FRACTIONAL BESSEL EQUATIONAND ITS ASYMPTOTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

Xiao-Li Ding, Yao-Lin JiangWAVEFORM RELAXATION METHODS FORFRACTIONAL FUNCTIONALDIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

T. TrifEXISTENCE OF SOLUTIONS TO INITIAL VALUEPROBLEMS FOR NONLINEAR FRACTIONALDIFFERENTIAL EQUATIONS ON THE SEMI-AXIS . . . . . . . . . . . . . 595

R. Abu-Saris, Q. Al-MdallalON THE ASYMPTOTIC STABILITY OF LINEAR SYSTEMOF FRACTIONAL-ORDER DIFFERENCE EQUATIONS . . . . . . . . . 613



T. Morita, K. SatoLIOUVILLE AND RIEMANN-LIOUVILLEFRACTIONAL DERIVATIVES VIACONTOUR INTEGRALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630

C. Gong, W. Bao and G. TangA PARALLEL ALGORITHM FOR THE RIESZFRACTIONAL REACTION-DIFFUSION EQUATIONWITH EXPLICIT FINITE DIFFERENCE METHOD . . . . . . . . . . . . . 654

T. Marinov, N. Ramirez, F. SantamariaFRACTIONAL INTEGRATION TOOLBOX . . . . . . . . . . . . . . . . . . . . . . 670

Y. Chalco-Cano, J.J. Nieto, A. Ouahab, H. Roman-FloresSOLUTION SET FOR FRACTIONAL DIFFERENTIALEQUATIONS WITH RIEMANN-LIOUVILLE DERIVATIVE . . . . . . 682

J.R. Graef, L. KongEXISTENCE OF POSITIVE SOLUTIONS TO A HIGHERORDER SINGULAR BOUNDARY VALUE PROBLEMWITH FRACTIONAL Q-DERIVATIVES . . . . . . . . . . . . . . . . . . . . . . . . . . 695

Yufeng Xu, O.P. AgrawalNUMERICAL SOLUTIONS AND ANALYSIS OFDIFFUSION FOR NEW GENERALIZED FRACTIONALBURGERS EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709

G. Baumann, F. StengerFRACTIONAL ADSORPTION DIFFUSION . . . . . . . . . . . . . . . . . . . . . . 737


CONTENTS

Editorial:V. Kiryakova, J.J. O’Connor, E.F. Robertson, D. Nemzer

FCAA RELATED EVENTS AND 100th ANNIVERSARYOF THE BIRTH OF JAN MIKUSINSKI(FCAA–Volume 16–4–2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765

Z.D. Mei, J.G. Peng, Y. ZhangA CHARACTERISTIC OF FRACTIONAL RESOLVENTS . . . . . . . . 777

S. Kumar, N. SukavanamCONTROLLABILITY OF FRACTIONAL ORDER SYSTEMWITH NONLINEAR TERMHAVING INTEGRAL CONTRACTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791

S. Roscani, E. Santillan MarcusTWO EQUIVALENT STEFAN’S PROBLEMSFOR THE TIME FRACTIONAL DIFFUSION EQUATION . . . . . . . 802

A.M.A. El-Sayed, H.H.G. HashemEXISTENCE RESULTS FOR NONLINEAR QUADRATICINTEGRAL EQUATIONS OF FRACTIONAL ORDERIN BANACH ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816

T.M. Michelitsch, G.A. Maugin,A.F. Nowakowski, F.C.G.A. Nicolleau, M. Rahman

THE FRACTIONAL LAPLACIAN AS A LIMITING CASEOF A SELF-SIMILAR SPRING MODELAND APPLICATIONS TO N -DIMENSIONALANOMALOUS DIFFUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827

A.N. KochubeiFRACTIONAL-HYPERBOLIC SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . 860



N.J. Ford, M.L. Morgado, M. RebeloNONPOLYNOMIAL COLLOCATION APPROXIMATIONOF SOLUTIONS TO FRACTIONALDIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874

I. Karatay, N. Kale, S.R. BayramogluA NEW DIFFERENCE SCHEME FOR TIMEFRACTIONAL HEAT EQUATIONS BASED ONTHE CRANK-NICHOLSON METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892

R.R. Nigmatullin, D. BaleanuNEW RELATIONSHIPS CONNECTINGA CLASS OF FRACTAL OBJECTS ANDFRACTIONAL INTEGRALS IN SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . 911

K. Zhang and J. XuUNIQUE POSITIVE SOLUTION FOR A FRACTIONALBOUNDARY VALUE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937

D. Rajter-Ciric, M. StojanovicFRACTIONAL DERIVATIVES OF MULTIDIMENSIONALCOLOMBEAU GENERALIZED STOCHASTIC PROCESSES . . . . . 949

A. Aghajani, E. Pourhadi, J.J. TrujilloAPPLICATION OF MEASURE OF NONCOMPACTNESSTO A CAUCHY PROBLEM FOR FRACTIONALDIFFERENTIAL EQUATIONS IN BANACH SPACES . . . . . . . . . . . . 962

R.A.C. FerreiraA LYAPUNOV-TYPE INEQUALITY FOR A FRACTIONALBOUNDARY VALUE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978

J. Henderson, R. LucaPOSITIVE SOLUTIONS FOR A SYSTEM OF NONLOCALFRACTIONAL BOUNDARY VALUE PROBLEMS . . . . . . . . . . . . . . . . 985


CONTENTS

Editorial: FCAA RELATED NEWS, EVENTS AND BOOKS(FCAA–Volume 17–1–2014) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

J.-S. Duan, Z. Wang, S.-Z. FuTHE ZEROS OF THE SOLUTIONS OF THE FRACTIONALOSCILLATION EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

H. Yang, X. Zhu, K. CaoDISTRIBUTED COORDINATION OF FRACTIONALORDER MULTI-AGENT SYSTEMSWITH COMMUNICATION DELAYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Z. Tomovski, R. GarraANALYTIC SOLUTIONS OF FRACTIONALINTEGRO-DIFFERENTIAL EQUATIONS OF VOLTERRATYPE WITH VARIABLE COEFFICIENTS . . . . . . . . . . . . . . . . . . . . . . . . 38

Z.S.I. MansourON A CLASS OF NONLINEAR VOLTERRA–FREDHOLMq-INTEGRAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

M.-Ha Kim, G.-Chol Ri, H.-Chol OOPERATIONAL METHOD FOR SOLVING MULTI-TERMFRACTIONAL DIFFERENTIAL EQUATIONS WITHTHE GENERALIZED FRACTIONAL DERIVATIVES . . . . . . . . . . . . . 79

T.D. Ke, D. LanDECAY INTEGRAL SOLUTIONS FOR A CLASSOF IMPULSIVE FRACTIONAL DIFFERENTIALEQUATIONS IN BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Y. PovstenkoSOLUTIONS TO THE FRACTIONAL DIFFUSION-WAVEEQUATION IN A WEDGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122



Y.D. Ma, J.G. Lu, W.D. Chen, Y.Q. ChenA ROBUST STABILITY BOUNDS OF UNCERTAINFRACTIONAL-ORDER SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

A. Prasad, V.K. SinghBOUNDEDNESS OF PSEUDO-DIFFERENTIALOPERATOR ASSOCIATED WITHFRACTIONAL HANKEL TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . . . 154

R. Stern, F. Effenberger, H. Fichtner, T. SchaferTHE SPACE-FRACTIONAL DIFFUSION-ADVECTIONEQUATION: ANALYTICAL SOLUTIONS AND CRITICALASSESSMENT OF NUMERICAL SOLUTIONS . . . . . . . . . . . . . . . . . . . 171

C.M. Kirk, W.E. OlmsteadTHERMAL BLOW-UP IN A SUBDIFFUSIVE MEDIUMDUE TO A NONLINEAR BOUNDARY FLUX . . . . . . . . . . . . . . . . . . . . 191

M. FabrizioFRACTIONAL RHEOLOGICAL MODELSFOR THERMOMECHANICAL SYSTEMS.DISSIPATION AND FREE ENERGIES . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

C.A. TudorRECENT DEVELOPMENTS ON STOCHASTICHEAT EQUATION WITH ADDITIVEFRACTIONAL-COLORED NOISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

A.A. Khamzin, R.R. Nigmatullin, I.I. PopovJUSTIFICATION OF THE EMPIRICAL LAWS OF THEANOMALOUS DIELECTRIC RELAXATION IN THEFRAMEWORK OF THE MEMORY FUNCTION FORMALISM . . 247

S. Arshad, V. Lupulescu, D. O’ReganLP -SOLUTIONS FOR FRACTIONALINTEGRAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

S. SamkoRemark to the paper of S. Samko, “A NOTE ON RIESZFRACTIONAL INTEGRALS IN THE LIMITING CASEα(x)p(x) ≡ n”, from FCAA, Vol. 16, No 2, 2013 . . . . . . . . . . . . . . . . . . . 277


CONTENTS


N.D. Cong, T.S. Doan, H.T. TuanON FRACTIONAL LYAPUNOV EXPONENTFOR SOLUTIONS OF LINEARFRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . 285

T. Blaszczyk, M. CiesielskiNUMERICAL SOLUTION OF FRACTIONALSTURM–LIOUVILLE EQUATION IN INTEGRAL FORM . . . . . . . . 307

C. Zeng, Y.Q. ChenOPTIMAL RANDOM SEARCH, FRACTIONAL DYNAMICSAND FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

S. Choudhary, V. Daftardar-GejjiNONLINEAR MULTI-ORDER FRACTIONALDIFFERENTIAL EQUATIONS WITH PERIODIC/ANTI-PERIODIC BOUNDARY CONDITIONS . . . . . . . . . . . . . . . . . . . . 333

B. Ahmad, S. NtouyasA FULLY HADAMARD TYPE INTEGRAL BOUNDARYVALUE PROBLEM OF A COUPLED SYSTEMOF FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . 348

R. HerrmannTOWARDS A GEOMETRIC INTERPRETATIONOF GENERALIZED FRACTIONAL INTEGRALS –ERDELYI-KOBER TYPE INTEGRALS ON RN ,AS AN EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

S. Roscani, E. Santillan MarcusA NEW EQUIVALENCE OF STEFAN’S PROBLEMSFOR THE TIME FRACTIONAL DIFFUSION EQUATION . . . . . . 371



N. Khodabakhshi, S.M. Vaezpour, D. BaleanuNUMERICAL SOLUTIONS OF THE INITIAL VALUE PROBLEMFOR FRACTIONAL DIFFERENTIAL EQUATIONS BY MODIFI-CATION OF THE ADOMIAN DECOMPOSITION METHOD . . . . . 382

M. Jelassi, H. MejjaoliFRACTIONAL SOBOLEV TYPE SPACES ASSOCIATED WITH ASINGULAR DIFFERENTIAL OPERATOR AND APPLICATIONS 401

R. Garra, A. Giusti, F. Mainardi, G. PagniniFRACTIONAL RELAXATION WITHTIME-VARYING COEFFICIENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

M.S. TavazoeiTIME RESPONSE ANALYSIS OF FRACTIONAL-ORDERCONTROL SYSTEMS: A SURVEY ON RECENT RESULTS . . . . . . 440

I. Tejado, S.H. HosseinNia, B.M. VinagreADAPTIVE GAIN-ORDER FRACTIONAL CONTROL FORNETWORK-BASED APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

M. Al-Refai, Yu. LuchkoMAXIMUM PRINCIPLE FOR THE FRACTIONAL DIFFUSIONEQUATIONS WITH THE RIEMANN-LIOUVILLE FRACTIONALDERIVATIVE AND ITS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 483

J.R. Graef, L. Kong, M. WangEXISTENCE AND UNIQUENESS OF SOLUTIONS FOR AFRACTIONAL BOUNDARY VALUE PROBLEM ON A GRAPH . 499

K. Balachandran, V. Govindaraj,L. Rodrıguez-Germa, J.J. TrujilloSTABILIZABILITY OF FRACTIONALDYNAMICAL SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

A. Kerss, N.N. Leonenko, A. SikorskiiFRACTIONAL SKELLAM PROCESSESWITH APPLICATIONS TO FINANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . 532

D. Valerio, J. Tenreiro Machado, V. KiryakovaSOME PIONEERS OF THE APPLICATIONSOF FRACTIONAL CALCULUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552


CONTENTS


Xiao-Li Ding, Yao-Lin JiangWAVEFORM RELAXATION METHOD FOR FRACTIONALDIFFERENTIAL-ALGEBRAIC EQUATIONS . . . . . . . . . . . . . . . . . . . . . 585

W. Sun, Y. WangMULTIPLE POSITIVE SOLUTIONS OF NONLINEARFRACTIONAL DIFFERENTIAL EQUATIONS WITHINTEGRAL BOUNDARY VALUE CONDITIONS . . . . . . . . . . . . . . . . . 605

W. Zhang, W. Wei, X. CaiPERFORMANCE MODELING OF SERIAL ANDPARALLEL IMPLEMENTATIONS OF THE FRACTIONALADAMS-BASHFORTH-MOULTON METHOD . . . . . . . . . . . . . . . . . . . . 617

K.R. Prasad, B.M.B. KrushnaEIGENVALUES FOR ITERATIVE SYSTEMS OFSTURM-LIOUVILLE FRACTIONAL ORDER TWO-POINTBOUNDARY VALUE PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638

S. Dubey, M. SharmaSOLUTIONS TO FRACTIONAL FUNCTIONALDIFFERENTIAL EQUATIONSWITH NONLOCAL CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654

Yu.A. Rossikhin, M.V. ShitikovaCENTENNIAL JUBILEE OF ACADEMICIAN RABOTNOVAND CONTEMPORARY HANDLINGOF HIS FRACTIONAL OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674

Yu.N. Rabotnov (Transl. in EN by M. Shitikova)EQUILIBRIUM OF AN ELASTIC MEDIUM WITH AFTER-EFFECT(Reprinted from Prikladnaya Matematika i Mekhanika (J. Appl. Math.Mech.) 12, No 1 (1948), 53-62, In Russian) . . . . . . . . . . . . . . . . . . . . . . . . 684



E.Gonzalez, L. Dorcak, C.A.Monje, J. Valsa, F.Caluyo, I. PetrasCONCEPTUAL DESIGN OF A SELECTABLEFRACTIONAL-ORDER DIFFERENTIATORFOR INDUSTRIAL APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697

G. Bonanno, R. Rodrıguez-Lopez, S. TersianEXISTENCE OF SOLUTIONS TO BOUNDARYVALUE PROBLEM FOR IMPULSIVE FRACTIONALDIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717

S. Umarov, F. Daum, K. NelsonFRACTIONAL GENERALIZATIONS OF FILTERING PROBLEMSAND THEIR ASSOCIATED FRACTIONAL ZAKAI EQUATIONS 745

B. RubinTHE λ-COSINE TRANSFORMS WITH ODD KERNELAND THE HEMISPHERICAL TRANSFORM . . . . . . . . . . . . . . . . . . . . . 765

C.A. Tudor, M. ZiliCOVARIANCE MEASURE AND STOCHASTIC HEATEQUATION WITH FRACTIONAL NOISE . . . . . . . . . . . . . . . . . . . . . . . . 807

C. Chen, M. Kostic, M. LiREPRESENTATION OF COMPLEX POWERSOF C-SECTORIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827

P. Eloe, J. NeugebauerCONJUGATE POINTS FOR FRACTIONALDIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855

J. Henderson, N. KosmatovEIGENVALUE COMPARISON FOR FRACTIONAL BOUNDARYVALUE PROBLEMS WITH THE CAPUTO DERIVATIVE . . . . . . . 872

A.N. KochubeiASYMPTOTIC PROPERTIES OF SOLUTIONS OFTHE FRACTIONAL DIFFUSION-WAVE EQUATION . . . . . . . . . . . . 881

A. Karapetyants, F. KodzoevaCHARACTERIZATION OF WEIGHTED ANALYTICBESOV SPACES IN TERMS OF OPERATORSOF FRACTIONAL DIFFERENTIATION . . . . . . . . . . . . . . . . . . . . . . . . . 897


CONTENTS

SPECIAL ISSUE:

Dedicated to 80th Anniversary of Prof. Ivan Dimovski


I. DimovskiNONCLASSICAL CONVOLUTIONS AND THEIR USES . . . . . . . . . 936

Yu. TsankovA THEOREM OF UNIQUENESS OF THE SOLUTION OFNONLOCAL EVOLUTION BOUNDARY VALUE PROBLEM . . . . . 945

E. Bazhlekova, I. BazhlekovVISCOELASTIC FLOWS WITH FRACTIONALDERIVATIVE MODELS: COMPUTATIONAL APPROACHBY CONVOLUTIONAL CALCULUS OF DIMOVSKI . . . . . . . . . . . . . 954

V. KiryakovaFROM THE HYPER-BESSEL OPERATORS OF DIMOVSKITO THE GENERALIZED FRACTIONAL CALCULUS . . . . . . . . . . . 977

J. Paneva-KonovskaA FAMILY OF HYPER-BESSEL FUNCTIONSAND CONVERGENT SERIES IN THEM . . . . . . . . . . . . . . . . . . . . . . . . 1001

R. Rodrıguez-Lopez, S. TersianMULTIPLE SOLUTIONS TO BOUNDARY VALUEPROBLEM FOR IMPULSIVEFRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . 1016

T. Atanackovic, D. Dolicanin, S. Pilipovic, B. StankovicCAUCHY PROBLEMS FOR SOME CLASSES OF LINEARFRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . 1039



D. NemzerEXTENDING THE STIELTJES TRANSFORM II . . . . . . . . . . . . . . . . 1060

S. Esmaeili, G.V. MilovanovicNONSTANDARD GAUSS–LOBATTO QUADRATUREAPPROXIMATION TO FRACTIONAL DERIVATIVES . . . . . . . . . . 1075

Dj. Takaci, A. Takaci, Al. TakaciON THE OPERATIONAL SOLUTIONS OFFUZZY FRACTIONAL DIFFERENTIAL EQUATIONS . . . . . . . . . . 1100

Z. Li, Yu. Luchko, M. YamamotoASYMPTOTIC ESTIMATES OF SOLUTIONSTO INITIAL-BOUNDARY-VALUE PROBLEMSFOR DISTRIBUTED ORDER TIME-FRACTIONALDIFFUSION EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114

A.H. Bhrawy, Y.A. Alhamed, D. Baleanu, A.A. Al-ZahraniNEW SPECTRAL TECHNIQUES FOR SYSTEMSOF FRACTIONAL DIFFERENTIAL EQUATIONSUSING FRACTIONAL-ORDER GENERALIZEDLAGUERRE ORTHOGONAL FUNCTIONS . . . . . . . . . . . . . . . . . . . . . 1137

Shengli XieEXISTENCE RESULTS OF MILD SOLUTIONS FORIMPULSIVE FRACTIONAL INTEGRO-DIFFERENTIALEVOLUTION EQUATIONS WITH INFINITE DELAY . . . . . . . . . . . 1158

Z. B. Bai, Y. Q. Chen, H. R. Lian, S. J. SunON THE EXISTENCE OF BLOW UP SOLUTIONS FORA CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS . . . . 1175

J. Tenreiro Machado, A.M. Lopes, F.B. Duarte,M.D. Ortigueira, R.T. RatoRHAPSODY IN FRACTIONAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1188

R. HerrmannREFLECTION SYMMETRIC ERDELYI-KOBER TYPEOPERATORS – A QUASI-PARTICLE INTERPRETATION . . . . . . 1215

Documents

CONTENTS OF ALL VOLUMES of “FCAA” Vol. 1 (1998) – Vol. 17 ...fcaa/CONTENTS_FCAA_ALL.pdf · CONTENTS OF ALL VOLUMES of “FCAA” Vol. 1 (1998) – Vol. 17 (2014) Managing Editor: