Existence results for a coupled system of Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions

Abstract

Abstract This paper is concerned with the existence and uniqueness of solutions for a coupled system of Liouville–Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions. The fractional integro-differential equations involve Caputo derivative operators of different orders and finitely many Riemann–Liouville fractional integral and non-integral type nonlinearities. The boundary conditions at the terminal position t = 1 $t=1$ involve sub-strips and multi-point contributions. The Banach fixed point theorem and the Leray–Schauder alternative are used to establish our results. The obtained results are illustrated with the aid of examples.

Keywords

• Caputo derivative
• Riemann–Liouville integral
• Coupled system
• Multi-point boundary conditions
• Existence
• Fixed point theorem