Stability of $\psi$-Hilfer Impulsive Fractional Differential Equations

TL;DR

This paper studies the existence, uniqueness, and stability of solutions for impulsive fractional differential equations involving the $\psi$-Hilfer derivative, using fixed point methods to establish key theoretical results.

Contribution

It provides new sufficient conditions for solution existence, uniqueness, and stability of $\psi$-Hilfer impulsive fractional differential equations, expanding the theoretical framework.

Findings

Established conditions for solution existence and uniqueness.

Proved $\delta$-Ulam-Hyers-Rassias stability under certain conditions.

Applied fixed point theory to fractional impulsive equations.

Abstract

In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and {\delta}-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $\psi$-Hilfer fractional derivative. Fixed point approach is used to obtain our main results.