Unified approach to uniqueness of solutions for a coupled system of fractional differential equations with three types of boundary value conditions

Abstract

This paper presents a unified approach to investigate a coupled system of Caputo fractional differential equations with three types of boundary conditions: multi-point, infinite-point, and Riemann–Stieltjes integral boundary conditions. Under a generalized Lipschitz condition, we first prove the uniqueness of solutions for the system with multi-point boundary conditions via the Banach contraction mapping principle. By taking limits, we obtain the existence of solutions for the remaining two boundary conditions directly without requiring any additional proof. The feasibility of this limiting argument lies in overcoming the complexity of the associated space and operator. Finally, numerical examples verify the theoretical findings.