Existence and stability results of relaxation fractional differential equations with Hilfer--Katugampola fractional derivative.

Year 2020, , 299 - 315, 30.12.2020

Mohammed Almalahı , Satish K. Panchal

https://doi.org/10.31197/atnaa.686693

Cited By: 1

Abstract

In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional
differential equations involving Hilfer-Katugampola derivative subject to nonlocal fractional integral bound-
ary conditions. The reasoning is mainly based upon properties of Mittag-Leffler functions, and fixed-point
methods such as Banach contraction principle and Krasnoselskii's fixed point theorem. Moreover, the gener-
alized Gornwall inequality lemma is used to analyze different types of stability. Finally, one example is given
to illustrate our theoretical results.

Keywords

Hilfer--Katugampola fractional derivative, Existence, Mittag-Leffler functions, Ulam stability

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