Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

Abstract

In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results.

Keywords

• Caputo fractional derivative
• Riemann–Liouville fractional integral
• coupled system
• existence
• uniqueness
• fixed point theorem
• Hyers–Ulam stability.