Existence and uniqueness results for a coupled fractional order systems with the multi-strip and multi-point mixed boundary conditions

Abstract

Abstract This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations supplemented with the multi-strip and multi-point mixed boundary conditions. The existence of solutions is derived by applying Leray-Schauder’s alternative, while the uniqueness of the solution is established via Banach’s contraction principle. We also show the existence and uniqueness results of a positive solution by applying the Krasnoselskii fixed point theorem.

Keywords

• fractional differential systems
• Leray-Schauder’s alternative
• fixed point theorems
• multi-strip and multi-point mixed boundary conditions