Generalized fractional derivatives and Laplace transform

Fahd Jarad; Thabet Abdeljawad

doi:10.3934/dcdss.2020039

Article Contents

2020, Volume 13, Issue 3: 709-722. Doi: 10.3934/dcdss.2020039

This issue Previous Article Variational principles in the frame of certain generalized fractional derivatives Next Article Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative

Generalized fractional derivatives and Laplace transform

Fahd Jarad^1, , and
Thabet Abdeljawad^2,3,4, ,

1.
Department of Mathematics, Çankaya University 06790, Ankara, Turkey
2.
Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

^* Corresponding author
^* Corresponding author

Received: July 31, 2018

Revised: September 30, 2018

Published: December 2019

The second author would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17

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Abstract

In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.

Keywords:

Generalized fractional derivatives,
generalized Caputo fractional derivative,
generalized Laplace transform.

Mathematics Subject Classification: Primary: 26A33; Secondary: 44A10.

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References

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