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 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

Kaynakça

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