On the existence and stability for non-instantaneuos impulsive fractional integrodifferential equation

TL;DR

This paper investigates the existence and stability of non-instantaneous impulsive fractional integrodifferential equations using the Banach fixed point theorem and $$-Hilfer fractional derivative, supported by illustrative examples.

Contribution

It introduces new results on the existence and Ulam--Hyers--Rassias stability for such equations employing $$-Hilfer derivatives, expanding the theoretical framework.

Findings

Established conditions for existence and stability

Provided illustrative examples confirming theoretical results

Extended the application of fixed point theorems to fractional impulsive equations

Abstract

In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam--Hyers--Rassias stability of the non-instantaneous impulsive integrodifferential equation by means of $\psi$-Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained.