Fundamental Results on Systems of Fractional Differential Equations Involving Caputo-Fabrizio Fractional Derivative

Abstract

In this paper, we analyze the solutions of a linear system of fractional differential equations involving the Caputo-Fabrizio fractional derivative. We first transform the system to a equivalent system of integro-differential equations with integer derivative. We then establish a uniqueness result for the system of fractional differential equations and present a necessary condition to guarantee the existence of a solution. Moreover, if the solution exists, the unique solution of the fractional system is obtained explicitly and is given in a closed form. Two examples are presented to illustrate the validity of the obtained results.

Key words and phrases. Systems of fractional differential equations, Caputo-Fabrizio fractional derivative.