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Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative

Fractional Integro-Differential Equations Involving $\psi$-Hilfer Fractional Derivative
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Year:    2019

Author:    Mohammed S. Abdo, Satish K. Panchal

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 338–359

Abstract

Considering a fractional integro-differential equation involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem. An example is provided to illustrate our main results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0143

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 338–359

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Fractional integro-differential equations $\psi$-Hilfer fractional derivative and $\psi$-fractional integral existence uniqueness and Ulam-Hyers stability fixed point theorem.

Author Details

Mohammed S. Abdo

Satish K. Panchal

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