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.