Ulam-Hyers-Rassias stability for a class of fractional integro-differential equations

TL;DR

This paper studies the stability of a specific class of fractional integro-differential equations using the recent $$-Hilfer derivative and fixed-point theorem, focusing on Ulam-Hyers and related stabilities on finite and infinite intervals.

Contribution

It introduces new stability results for fractional integro-differential equations employing the $$-Hilfer derivative and fixed-point methods, extending existing stability concepts.

Findings

Established Ulam-Hyers stability for the equations.

Proved Ulam-Hyers-Rassias stability under certain conditions.

Demonstrated stability on both finite and infinite intervals.

Abstract

By means of the recent $\psi$-Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rassias on closed intervals $[a,b]$ and $[a,\infty)$ for a particular class of fractional integro-differential equations.