The uniqueness of solution for initial value problems for fractional differential equation involving the Caputo-Fabrizio derivative

Abstract

In this paper, we study some results about the expression of solutions to some linear differential equations for the CaputoFabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.