Four-point boundary value problems for a coupled system of fractional differential equations with $\psi$-Caputo fractional derivatives

TL;DR

This paper investigates the existence and uniqueness of solutions for a coupled system of fractional differential equations with four-point boundary conditions involving $$-Caputo derivatives, using fixed point theorems.

Contribution

It introduces new results on solution existence and uniqueness for such fractional systems with four-point boundary conditions, employing Leray-Schauder and Banach fixed point theorems.

Findings

Established conditions for existence and uniqueness of solutions.

Provided illustrative examples demonstrating applicability.

Extended fractional boundary value problem theory to coupled systems.

Abstract

In this paper, we focus on the existence and uniqueness of solutions of boundary value problems for a coupled system of fractional differential equations with four-point boundary conditions involving $\psi$-Caputo fractional derivatives. Our investigation is based on Leray-Schauder alternative and Banach's fixed point theorem. Two examples are presented to illustrate the applicability of the results developed.