Existence and stability results for a sequential $\psi$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

TL;DR

This paper investigates the existence, uniqueness, and stability of solutions for a class of nonlinear sequential $$-Hilfer fractional integro-differential equations with nonlocal boundary conditions, using fixed point theorems.

Contribution

It introduces new existence and stability results for these fractional equations employing multiple fixed point theorems, expanding the theoretical understanding of such problems.

Findings

Existence of solutions established via Banach contraction principle.

Uniqueness of solutions proved using Sadovski's fixed point theorem.

Ulam-Hyers stability of solutions demonstrated.

Abstract

This paper deals with the existence and uniqueness of solutions for a nonlinear boundary value problem involving a sequential $\psi$-Hilfer fractional integro-differential equations with nonlocal boundary conditions. The existence and uniqueness of solutions are established for the considered problem by using the Banach contraction principle, Sadovski's fixed point theorem, and Krasnoselskii-Schaefer fixed point theorem due to Burton and Kirk. In addition, the Ulam-Hyers stability of solutions is discussed. Finally, the obtained results are illustrated by examples.