Properties of the Caputo-Fabrizio Fractional Derivative,

Abstract

In this paper, we investigate some properties related CaputoFabrizio fractional derivative. We prove some regularity properties and bounds characterizing the Caputo-Fabrizio derivative operator. Using the method of Laplace transform, we found explicit solutions of some differential equations containing the Caputo-Fabrizio fractional derivative. Different types of inequalities generated by using the Caputo-Fabrizio derivative are also presented.