Existence Theoremsfor Solutions of a Nonlinear Fractional-Order Coupled Delayed System via Fixed Point Theory

Abstract

In this paper, the problem of the existence and uniqueness of solutions for a nonlinear fractional-order coupled delayed system with a new kind of boundary condition is studied. For this reason, we transform the above problem into an equivalent fixed point problem using the integral operator. Moreover, by applying fixed point theorems, a novel set of sufficient conditions that guarantee the existence and uniqueness of solutions of the coupled system is derived. Eventually, an example is presented to illustrate the effectiveness of the obtained results.