Leray–Schauder Alternative for the Existence of Solutions of a Modified Coupled System of Caputo Fractional Differential Equations with Two Point’s Integral Boundary Conditions

Abstract

In this paper, a coupled system of differential equations involving fractional order with integral boundary conditions is discussed. In the problem at hand, three main aspects that are existence, uniqueness, and stability have been investigated. Firstly, the contraction mapping principle is used to discuss the uniqueness of solutions for the proposed fractional system, and secondly, the existence of solutions for the problem is investigated based on Leray–Schauder’s alternative. Thirdly, the stability of the presented coupled system is discussed based on the Hyers–Ulam stability method. Finally, some examples have been given to confirm and illustrate the conclusion. The comparison between the current symmetrical results and the existing literature is deemed satisfactory. It was found that the presented fractional coupled system with two with integral boundary conditions is existent, unique, and stable.

Keywords

• fractional differential
• contraction mapping principle
• Hyers-Ulam stability
• fractional differential equation