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29May
2020
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https://doi.org/10.22541/au
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$\psi$–Katugampola Fractional Derivatives andIntegrals-Application to Mass–Spring Damper System
Ramazan OZARSLAN1, Yadigar Sekerci2, and Erdal BAS1
1Firat Universitesi2Amasya University
May 29, 2020
Abstract
We propose a new type of generalized fractional derivatives with respect to (wrt) another function. These new generalized
fractional derivatives generalize $\psi$–Caputo, Riemann–Liouville (R–L) wrt another function, Caputo Hadamard wrt anotherfunction, R–L Hadamard wrt another function, Caputo, R–L, Caputo Hadamard and R–L Hadamard fractional derivatives. We
propose a newly modified Laplace transform for linear $\psi$–Katugampola fractional differential equations (FDEs). Propertiesof this newly generalized Laplace transform are analyzed. Cauchy problems and mass-spring damper system with $\psi$–Katugampola fractional derivative are solved analytically by means of modified Laplace transform. Finally, a new numerical
method is proposed for nonlinear $\psi$–Katugampola FDEs.
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https://authorea.com/users/327906/articles/455299--psi-katugampola-fractional-derivatives-and-integrals-application-to-mass-spring-damper-systemhttps://authorea.com/users/327906/articles/455299--psi-katugampola-fractional-derivatives-and-integrals-application-to-mass-spring-damper-system
Postedon
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29May
2020
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