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

Abstract

In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractionaldifferential 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-pointmethods 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 givento illustrate our theoretical results.