Unique Solution for a General Coupled System of Fractional Differential Equations

Abstract

This paper discusses a new coupled system of Riemann-Liouville fractional differential equations, in which the nonlinear terms include the Riemann-Liouville fractional integrals and the boundary value problems involve three-points. We seek also for the existence and uniqueness of solutions for this new system. We first get some useful properties of the Green’s function generated by the system, and then we apply a fixed point theorem of increasing $φ$-$(h, e)$-concave operators to this new coupled system. Finally, we gain the existence and uniqueness results of the solution for this problem. In the end, a concrete example is structured to illustrate the main result.