EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A COUPLED DIFFERENTIAL SYSTEM INVOLVING CAPUTO-FABRIZIO FRACTIONAL DERIVATIVES

In this paper, we establish the existence and uniqueness of solutions for a system of coupled differential equations of arbitrary order subject to nonlinear boundary conditions within generalized Banach spaces. The fractional derivatives used are of Caputo-Fabrizio type. We provide the exact solution for an auxiliary boundary value problem and use this expression for the analysis of the nonlinear problem of interest. The analytical approach involves the application of the nonlinear alternative of Leray-Schauder type and the Banach contraction principle to a mapping whose fixed points are the solutions to the problem. Additionally, the paper concludes with an illustrative example to enhance understanding and highlight the practical implications of the obtained results.