SOLVABILITY AND STABILITY FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL SYSTEMS OF HIGHT FRACTIONAL ORDER

Abstract : In this paper, using Riemann-Liouville integral and Caputo derivative, we study an n-dimensional coupled system of nonlinear fractional integro-differential equations of hight arbitrary order. The contraction mapping principle and Schaefer fixed point theorem are applied to prove the existence and the uniqueness of solutions in Banach spaces. Furthermore, we derive the Ulam-Hyers and the generalized Ulam-Hyers stabilities of solutions. Some illustrative examples are also presented.