PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 1

1. Name and Address : Dr. KAPULA RAJENDRA PRASAD

Professor of Applied Mathematics

Andhra University

Visakhapatnam 530 003, INDIA

Phone No.s: +91-0891-2844533(O)

+ 91-0891-2537017(R)

+ 91-9849222496(M)

Email: rajendra92@rediffmail.com

2. Date of Birth : 20-11-1963

3. Educational Qualifications :

M.Sc. Applied Mathematics (Andhra University), 1985

Elective Subjects: Boundary Value Problems and Fluid Dynamics

Post B.Sc. (Diploma in Computer Science and Applications), 1986

Ph.D. Applied Mathematics (Andhra university), 1990

Title of Thesis: Contributions to Matrix Riccati Differential Equations and

Boundary Value Problems

4. Achievements :

University 3rd Rank in M.Sc. in the batch 1983-85

UGC-NET qualified, 1986

Junior Research Fellow from 1986 to 1988

Senior Research Fellow from 1988 to 1990

CSIR Research Associate from 1990 to 1994

BOYSCAST Fellowship Award of DST (Collaborative Research with Foreign

University and Worked with Prof. Johnny Henderson, Auburn University,

USA from March 1988 to September 1998

5. Broad Areas :

DIFFERENTIAL AND DIFFERENCE EQUATIONS

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 2

6. Research Areas :

Boundary Value Problems

Dynamic Equations on Time Scales

Fractional Order Boundary Value Problems

Mathematical Modeling

Qualitative and Quantitative Analysis of Differential Equations

Finite Difference Equations

7. List of Students Awarded Ph.D.

Degrees : 09

R. Suryanarayana ….. (2002)

P. Murali ….. (2010)

A. Kameswara Rao ….. (2010)

N. V. V. S. Suryanaraya ….. (2011)

S. Nageswara Rao ….. (2011)

K. L. Saraswathi Devi ….. (2012)

N. Sreedhar ….. (2015)

K. Rajendra Kumar ….. (2015)

B. Muralee Bala Krushna ….. (2015)

8. List of Students Awarded M.Phil.

Degrees : 10

M. N. Murthy ….. (1998)

B. Nagabhushana Rao ….. (1998)

N. V. V. S. Suryanarayana ….. (2003)

N. Sreedhar ….. (2005)

K. Bhaskara Rao ….. (2007)

K. Rajendra Kumar ….. (2008)

N. Sunil ….. (2009)

B. Muralee Bala Krushna ….. (2009)

B. Bharathi ….. (2013)

Md. Khuddush ….. (2015)

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 3

9. Membership in

Professional Societies :

Member in American Mathematical Society from 1998 onwards

Life Member in Indian Science Congress Association

Life Member in Andhra Pradesh State Mathematical Society

Life Member of International Society of Difference Equations

10. Research and

Professional Activities :

Worked as Junior Research Fellow from September 1986 to September 1988

Worked as Senior Research Fellow from September 1988 to January 1991

CSIR Research Associate Fellowship was Awarded in 1991 and worked

from January 1991 to March 1994

BOYSCAST Fellowship Award for collaborative research in USA by

DST, New Delhi and visited Auburn University, USA for SIX months in

1999

Published/Accepted/Communicated: 82 research papers in various National

and International Journals (List Enclosed)

Some of research contributions have appeared in the Recent Books,

Monographs and Dictionary of Differential Equations

Acted as Referee for Some National and International Journals like

a) Communications on Applied Nonlinear Analysis

b) Computers and Mathematics with Applications

c) Electronic Journal of Differential Equations

d) Electronic Journal of Qualitative Theory of Differential Equations

e) Boundary Value Problems

f) Advances in Difference Equations

g) Fractional Calculus and Applied Analysis

h) International Journal of Differential Equations

i) Differential Equations and Dynamical Systems

j) Journal of Applied Mathematics Letters

k) Journal of Applied Mathematics and Computing

Acted as Reviewer for

a) ZENTRABLAT Math

b) Mathematical Reviews

Acted as organizing committee member for conducting three International

Conference on “Nonlinear Analysis and Applications to Biomathematics”

Acted as Co-Chairman for conducting National Seminar on “Modern Trends

in Applied Mathematics (NSMTAM-2010)”

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 4

Acted as Chairman for conducting National Seminar on “Emerging Trends in

Applied Mathematics (NSETAM-2014)”

11. Teaching Experience :

Presently working as Professor, since January 2008

Worked as Associate Professor from January 2000 to January 2008

Worked as Assistant Professor from March 1994 to January 2000

Worked as Research Associate from January 1991 to March 1994

12. Subject Taught :

Differential Equations

Boundary value problems

Tensor Analysis

Methods of Applied Mathematics

Computer Programming Languages

Theoretical Computer Science

Elasticity

Higher Engineering Mathematics

13. Administrative Experience :

Presently working as Head of the Department of Applied Mathematics,

Andhra University, from April 2012 to till date

Presently working as Dean Confidential (Examinations), Andhra University,

from June 2013 to till date

Worked as Assistant Principal of College of Science & Technology for 3

years

Internal Auditor for IQAC from 2008 onwards

Acted as a Member in Confidential Academic Team in various Universities:

a) Andhra University, Visakhapatnam

b) Adikavi Nannaya University, Rajahmundry

c) Dr. B. R. Ambedkar University, Srikakulam

d) Krishna University, Machilipatnam

e) Vikrama Simhapuri University, Nellore

Acted as a Board of Studies Member for Various Universities:

a) JNTU (Hyderabad) for P.G. & U.G

b) ANU, Nuzividu

c) Berhampur University, Odisha

d) Central University, Koraput

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 5

e) G. V. P. College for Engineering, Visakhapatnam

f) Sri Padmavati Mahila Visvavidyalayam, Tirupati

14. Orientation/Refresher Courses: (Attended)

Participated in ISTE summer school on “Programming Methodology Modern

Trends in Software” from 01-05-1995 to 13-05-1995 (Two Weeks) held at

JNTU Kakinada

Participated in “Academic Staff Orientation Course” from 05-09-1995 to 30-

09-1995 (Four Weeks) held at Academic Staff College, Andhra university,

Visakhapatnam

Training and Collaborative Research in USA as BOYSCAST fellow

awarded by DST, India from 26-03-1999 to 25-09-1999 (Six Months) at

Auburn University, Auburn, USA

Participated in UGC Refresher Course in Applied Mathematics at Sri

Padmavathi Mahila Viswavidyalam, Tirupathi from 11-09-2002 to 01-10-

2002

15. Conferences/Seminars/Workshops : (Attended/Presented)

International Conference on “Nonlinear Analysis and Applications to

Biomathematics” from 24-28 August, 1987 held at Andhra University,

Visakhapatnam

Third Annual conference of the “Ramanujan Mathematical Society” from 27-

29 May, 1988 held at Manipal Institute of Technology, Manipal, Karnataka

Indian Science Congress Association, Young Scientist Award Session, from

3-8 January, 1993 held at Goa University, Goa

International Conference on “Nonlinear Analysis and Applications to

Biomathematics” from 24-28 August, 1993 held at Andhra University,

Visakhapatnam

International Conference on “Nonlinear Analysis and Applications to

Biomathematics” from 24-28 August, 1997 held at Andhra University,

Visakhapatnam

IV Mississippi State Conference on “Differential Equations and Computer

Simulation” from 21-22 May, 1999 held at Mississippi State University, USA

International Conference on “Dynamical Systems and Applications” from

July 1999 held at Georgia Technology University, Atlanta, USA

95th Indian Science Congress Association from 3-7, January 2008 held at

Andhra University, Visakhapatnam and Four papers were presented jointly

with Research Scholars

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 6

National Seminar on “Modern Trends in Applied Mathematics (NSMTAM-

2010)” held at Andhra University, from 9 -10, October 2010 and Three papers

were presented jointly with Research Scholars

National Conference on “Applications of Mathematics in Engineering

Sciences (NCAMES)-2011” held at Andhra University, from 29 -30, October

2011 and Two papers were presented jointly with Research Scholars

Andhra Pradesh Science Congress (APSC)-2011, which is jointly organized

by GITAM University and Andhra Pradesh Akademi of Sciences held at

GITAM University, Visakhapatnam from 14-16, November 2011 and paper

was presented jointly with Research Scholar

Mathematical Modeling in Natural and Physical Science, which is organized

by Department of Mathematics, Ch. S. D. St. Theresa’s Autonomous

College for Women, Eluru, from 16-17, November 2012 and Four papers

were presented jointly with Research Scholars

National Seminar on “Emerging Trends in Applied Mathematics (NSETAM-

2014)” held at Andhra University, from 4-5, April 2014 and Three papers

were presented jointly with Research Scholars

16. Conferences/Seminars/Workshops : (Conducted)

Acted as an organizing committee member for conducting International

Conference on “Nonlinear Analysis and Applications to Biomathematics”

from 24-28 August, 1987 held at Andhra University, Visakhapatnam

Acted as an organizing committee member for conducting International

Conference on “Nonlinear Analysis and Applications to Biomathematics”

from 24-28 August, 1993 held at Andhra University, Visakhapatnam

Acted as an organizing committee member for conducting International

Conference on “Nonlinear Analysis and Applications to Biomathematics”

from 24-28 August, 1997 held at Andhra University, Visakhapatnam

Acted as Co-Chairman for conducting National Seminar on “Modern Trends

in Applied Mathematics (NSMTAM-2010)” held at Andhra University, from

9 -10, October 2010

Acted as Chairman for conducting National Seminar on “Emerging Trends in

Applied Mathematics (NSETAM-2014)” held at Andhra University, from 4-

5, April 2014

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 7

17. List of Research Papers Published/Accepted:

1. A note on matrix Riccati functional differential equations, J. Math. Anal. Appl.,

1988, Vol. 132, No. 1, 50-56.

2. Certain mathematical models for biological systems and their approximate analytical

solutions, Proceedings of the International Conference on Non-Linear Analysis and

Applications to Biomathematics, Andhra University, 1987, 146-155.

3. A note on boundary value problems, Nepali Math. Sci. Rep., 1989, Vol. 14, No. 1-2,

41-48

4. Approximate analytical solutions to the three-species ecological system, J. Math.

Anal. Appl., 1990, Vol. 145, No.1, 89-99.

5. Upper and lower bounds for the solution of the general matrix Riccati differential

equations, J. Math. Anal. Appl., 1990, Vol. 147, No. 1, 12-21.

6. On the use of quasilinearization method in the growth of a pathogenic bacteria, J.

Math. Anal. Appl., 1990, Vol. 149, No. 2, 576-582.

7. Solution of a nonhomogeneous Liapunov’s equation, Tamkang J. Math., 1991, Vol.

22, No. 1, 31-38.

8. On the method of complementary functions for linear and nonlinear two-point

boundary value problems, J. Math. Anal. Appl., 1992, Vol. 167, No. 1, 32-42.

9. Kronecker product three-point (multi-point) boundary value problems-existence and

uniqueness, Bull. Inst. Math. Acad. Sinica, 1992, Vol. 20, No. 1, 83- 95.

10. On the use of differential inequalities in three-point boundary value problems, Bull.

Inst. Math. Acad. Sinica, 1993, Vol. 21, No. 3, 263-274.

11. Two-point boundary value problems associated with Liapunov type matrix

difference system, J. Dynam. Systems Appl., 1995, Vol.4, No. 2, 205-213.

12. Existence, uniqueness and sensitivity analysis of solutions of two-point boundary

value problem associated with nonlinear Liapunov type difference system, Int. J.

Nonlinear Anal. TMA, 1995, Vol. 1, 151-164.

13. Comparison of eigenvalues for Lidstone boundary value problems on a measure

chain, Comput. Math. Appl., 1999, Vol. 38, No. 11-12, 55-62.

14. Eigenvalue intervals for nonlinear right focal problems, Appl. Anal., 2000, Vol. 74,

No. 1-2, 215-231.

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 8

15. Matrix Ricatti difference equations associated with first order matrix difference

system, Engineering Simulations, 2000, Vol. 17, 347-357.

16. Eventual disconjugacy on time scales, Appl. Math. Lett., 2000, Vol. 13, No. 6, 77-82.

17. Nonlinear eigenvalue problems involving two classes of functional differential

equations, Houston J. Math., 2000, Vol. 26, No. 3, 597-608.

18. Solvability of a nonlinear conjugate eigenvalue problem, Canad. Appl. Math. Quart.,

2000, Vol. 8, No. 1, 27-42.

19. Solvability of a nonlinear second order conjugate eigenvalue problems on time scale,

Abstr. Appl. Anal., 2000, Vol. 5, No. 2, 91-99.

20. Matrix Ricatti differential equations on time scales, Comm. Appl. Nonlinear Anal.,

2001, Vol. 8, No. 1, 37-49.

21. Existence and uniqueness of solutions of three-point boundary value problems on

time scales by solution matching, Nonlinear Stud., 2001, Vol. 8, No. 1, 1-12.

22. Matrix Ricatti differential equations on time scales, Comm. Appl. Nonlinear Anal.,

2001, Vol. 8, No. 4, 63-75.

23. Nonlinear Kronecker product Lyapunov system existence, uniqueness and sensitivity

analysis, Math. Sci. Res. J., 2002, Vol. 6, No. 1, 30-46.

24. Upper and lower bounds for the solution of the general matrix Ricatti differential

equations on time scales, J. Comput. Appl. Math., 2002, Vol. 141, No. 1-2, 133-

145.

25. Kronecker product system of first order rectangular matrix differential equations-

existence and uniqueness, Bull. Inst. Math. Acad. Sinica, 2002, Vol. 30, No. 3, 205-

218.

26. Existence and uniqueness of solutions of two-point boundary value problems

associated with nonhomogeneous kronecker product Lyapunov system, Int. J.

Nonlinear Anal. TMA, 2002, Vol. 7, 105-119.

27. Multi-point boundary value problems associated with a first order nonlinear

Lyapunov system with periodic coefficients, Int. J. Nonlinear Anal. TMA, 2002, Vol.

7, 175-192.

28. Controllability and observability of kronecker product matrix Lyapunov system,

Differ. Equ. Dyn. Syst., 2005, Vol. 13, No. 3-4, 219-232.

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 9

29. Uniqueness implies existence for general three-point boundary value problems on

time scales, Comm. Appl. Nonlinear Anal., 2008, Vol. 15, No. 1, PP. 51-60.

30. Eigenvalue intervals for nth order differential equations on time scales, Int. J. Pure

Appl. Math., 2008, Vol. 44, No. 5, 737 - 753.

31. Multiple positive solutions for nonlinear third order general three-point boundary

value problems, Differ. Equ. Dyn. Syst., 2008, Vol. 16, No. 1-2, 63-75.

32. Multiple positive solutions for nonlinear third order general two-point boundary

value problems, Electron. J. Qual. Theory Differ. Equ., 2009, Vol. 2009, No. 9, 1-

17.

33. Multiple positive solutions for the system of higher order two-point boundary value

problems, Panamer. Math. J., 2009, Vol. 19, No. 2, 63-73.

34. Multiple positive solutions for the system of higher order two-point boundary value

problems on time scales, Electron. J. Qual. Theory Differ. Equ., 2009, Vol. 2009,

No. 32, 1-13.

35. Positive solution for third order three-point boundary value problems on time scales,

Int. J. Pure Appl. Math., 2009, Vol. 53, No. 3, 425–439.

36. Multiple positive solutions for nonlinear third order general two-point boundary

value problems on time scales, Int. J. Pure Appl. Math., 2009, Vol. 56, No. 2, 203-

216.

37. Existence of multiple positive solutions to three-point boundary value problems on

time scales, Int. J. Difference Equ.., 2009, Vol. 4, No. 2, 219-232.

38. Solvability of a nonlinear general third order two-point eigenvalue problem on time

scales, Differ. Equ. Dyn. Syst., 2009, Vol. 17, No. 3, 269-282.

39. Multiple positive solutions for nonlinear third order general three-point boundary

value problems on time scales, Comm. Appl. Nonlinear Anal., 2010, Vol. 17, No.

1, 1– 11.

40. Solvability for even-order three-point boundary value problems on time scales, Int.

J. Appl. Math., 2010, Vol. 23, No. 1, 23–41.

41. Solvability of a nonlinear third-order three-point general eigenvalue problem on time

scales. Electron. J. Differential Equations, 2010, Vol. 2010, No. 57, 1-12.

42. Eigenvalue intervals for two-point general third order differential equation, Bull.

Inst. Math. Acad. Sin. (New Series), 2010, Vol. 5, No. 1, 55-68.

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 10

43. Eigenvalue intervals for 3n-th order three-point boundary value problems, Int. J.

Pure Appl. Math., 2010, Vol. 61, No. 1, 79–94.

44. Multiple positive solutions for a nonlinear 3n-th order three-point boundary value

problem, Electron. J. Differential equations, 2010, Vol. 2010, No. 176, 1-12.

45. Even number of positive solutions for 3nth order three-point boundary value

problem, Commun. Appl. Anal., 2010, Vol. 14, No. 3-4, 393–407.

46. Multiple symmetric positive solutions for two-point even order boundary value

problems on time scales, Mathematics in Engineering, Science and Aerospace,

2010, Vol. 1, No. 1, 1 -13.

47. Multiple Positive Solutions for the Sturm-Liouville fractional order boundary value

problem. Panamerican Math. J., 2011, Vol. 21, No. 1, 99-108.

48. Eigenvalue intervals of two point boundary Problems for general nth order

differential equations, Nonlinear Stud., 2011, Vol. 19, No. 2, 167-176.

49. Multiple symmetric positive solutions for the systems of higher order boundary

value problems on time scales, Electron. J. Differential Equations, 2011, Vol. 2011,

No. 102, 1-12.

50. Even number of positive solutions for 3nth order three-point boundary value

problems on time scales, Electron. J. Qual. Theory Differ. Equ., 2011, Vol. 2011,

No. 98, 1-16.

51. Even number of symmetric positive solutions for the system of higher order

boundary value problems on time scales, Math. Commun., 2011, Vol. 19, No. 2, 455-

470.

52. Multiple symmetric positive solutions for Sturm-Liouville two-point boundary value

problems on time scales, Neural Parallel Sci. Comput., 2012, Vol. 20, No. 1, 51–64.

53. Existence of multiple positive solutions for 3nth order three-point boundary value

problems on time scales, Int. J. Open Problems Compt. Math., 2012, Vol. 5, No. 2,

72-87.

54. Existence of positive solutions for the system of higher order two-point boundary

value problems, Proc. Indian Acad. Sci. (Math. Sci.), 2012, Vol. 122, No. 1, 139-

152.

55. Heteroclinic solutions of singular 𝛷-Laplacian boundary value problems on

infinite time scales, Electron. J. Qual. Theory Differ. Equ., 2012, Vol. 2012, No. 68,

1-9.

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 11

56. Existence of positive solutions for the system of higher order two-point boundary

value problems on time scales, Int. J. Math. Sci. Eng. Appl., 2012, Vol. 6 No. 5,

235-250.

57. Solvability of p-Laplacian singular boundary value problems on time scales, Adv.

Pure Appl. Math., 2012, Vol. 3, No. 4, 377-391.

58. Solving third order three-point boundary value problem on time scales by solution

matching using differential inequalities, Global Journal of Science Frontier

Research Mathematics & Decision Sciences, 2012, Vol. 12, 91-101.

59. Upper and lower solutions for general two-point boundary value problems on time

scales, Neural Parallel Sci. Comput., 2013, Vol. 21, No. 1, 31–41.

60. Positive solutions for system of higher order singular nonlinear boundary value

problems, Math. Commun., 2013, Vol. 18, No. 1, 49-60.

61. Existence of positive solutions for higher order (p, q)-Laplacian two-point boundary

value problems, Int. J. Differ. Equ., 2013, Art. ID 743943, 1-9.

62. Existence of heteroclinic solutions to fourth order 𝛷-Laplacian dynamical equations,

Int. J. Anal. Appl., 2013, Vol. 3, No. 1, 47-52.

63. Even number of symmetric positive solutions for Sturm-Liouville two-point

boundary value problems on time scales, Bull. Int. Math. Virtual Inst., 2013, Vol. 3,

No. 1, 85-97.

64. Multiple positive solutions for a coupled system of Riemann-Liouville fractional

order two-point boundary value problems, Nonlinear Stud., 2013, Vol. 20, No. 4,

501-511.

65. Existence of multiple positive solutions for nth order two-point boundary value

problems on time scales, Advances in Pure Mathematics, 2013, Vol. 3, 70-77.

66. Solvability of iterative systems of three-point boundary value problems, TWMS J.

App. Eng. Math., 2013, Vol. 3, No. 2, 147-159.

67. Positive solutions for system of 2nth order Sturm-Liouville boundary value problems

on time scales, Proc. Indian Acad. Sci. (Math. Sci.), 2014, Vol. 124, No. 1, 67-79.

68. Eigenvalue intervals for iterative systems of nonlinear three-point boundary value

problems on time Scales, Nonlinear Stud., (accepted).

69. Solvability of Higher Order (p,q) Laplacian Two-Point Boundary Value Problems, J.

Appl. Computat. Math., 2014, Vol. 3, No. 6, 1-6, 182. doi: 10.4172/2168-

PROFILE OF Prof. K. RAJENDRA PRASAD

Department of Applied Mathematics, Andhra University, Visakhapatnam 12

9679.1000182.

70. Eigenvalue intervals for iterative systems of nonlinear m-point boundary value

problems on time Scales, Diff. Equ. Dyn. Syst., 2014, Vol. 22, No. 4, 353-368.

71. Eigenvalues for iterative systems of (n, p) - type fractional order boundary value

problems, Int. J. Anal. Appl., 2014, Vol. 5, No. 2, 136-146.

72. Existence of positive solutions for ternary system of higher order two-point

boundary value problems, Int. J. Anal. Appl., (accepted).

73. Multiple positive solutions for a coupled system of p-Laplacian fractional order

two-point boundary value problems, Int. J. Differ. Equ., 2014, Vol. 2014, Art. ID

485647, 1-10, http://dx.doi.org/10.1155/2014/485647.

74. Eigenvalues for iterative systems of Sturm-Liouville fractional order two-point

boundary value problems, Frac. Cal. Appl. Anal., 2014, Vol. 17, No. 3, 638-653.

75. Existence of multiple positive solutions for p-Laplacian fractional order boundary

value problems, Int. J. Anal. Appl., 2014, Vol. 6, No. 1, 63-81.

76. Existence of positive solutions for systems of second order multi-point boundary

value problems on time scales, Proc. Indian Acad. Sci. (Math. Sci.), (accepted).

77. Multiple positive solutions for the system of (n, p)-type fractional order boundary

value problems, Bull. Int. Math. Virtual Inst., 2015, Vol. 5, No. 1, 1-12.

78. Lower and upper solutions for general two-point fractional order boundary value

problems, TWMS J. App. Eng. Math., 2015, Vol. 5, No.1, 80-87.

79. Solvability of p-Laplacian fractional higher order two-point boundary value

problems, Commun. Appl. Anal., (accepted).

80. Nonexistence of positive solution for a system of nonlinear multi-point bvp on time

scales, Math. Commun., 2015, Vol. 20, No. 1, 69-81.

81. Existence of solutions for a coupled system of three-point fractional order boundary

value problems, Diff. Equ. Appl., 2015, Vol. 7 No. 2, 187-200.

82. Multiple positive solutions of higher order (p, q)-Laplacian Sturm-Liouvile type

boundary value problems, J. Nonlinear Fun. Anal., (accepted).