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$\psi$–Katugampola Fractional Derivatives and Integrals-Application to Mass–Spring Damper System
  • Ramazan OZARSLAN,
  • Yadigar Sekerci,
  • Erdal BAS
Ramazan OZARSLAN
Firat Universitesi
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Yadigar Sekerci
Amasya University
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Erdal BAS
Firat Universitesi
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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 another function, 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). Properties of 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.

Peer review status:IN REVISION

28 May 2020Submitted to Mathematical Methods in the Applied Sciences
29 May 2020Submission Checks Completed
29 May 2020Assigned to Editor
30 May 2020Reviewer(s) Assigned
17 Aug 2020Review(s) Completed, Editorial Evaluation Pending
17 Aug 2020Editorial Decision: Revise Major
23 Sep 20201st Revision Received
23 Sep 2020Assigned to Editor
23 Sep 2020Submission Checks Completed