Uniqueness and stability of coupled sequential fractional differential equations with boundary conditions

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Caputo-type sequential fractional differential equations supplemented with boundary conditions. The existence of solutions is derived by applying the Leray–Schauder alternative, while the uniqueness of solutions is established via Banach’s contraction principle. Moreover, some necessary conditions for the Hyers–Ulam-type stability to the solutions of the boundary value problem are developed. Finally the results are supported by example.