New aspects of Caputo-Fabrizio fractional derivative

In this paper, we consider classes of linear and nonlinear fractional differential equations involving the Caputo-Fabrizio fractional derivative of non-singular kernel. We transform the fractional problems to equivalent initial value problems with integer derivatives. We illustrate the obtained results by presenting two mathematical models of fractional differential equations and their equivalent initial value problems. We show that it is impossible to convert all types of linear fractional differential equations to the integer ones.The obtained results will lead to better understanding of fractional models, as the solutions of their equivalent models can be studied analytically and numerically using well-known techniques of differential equations.