On solutions of linear and nonlinear fractional differential equations with application to fractional order RC type circuits

Abstract

In this paper, we solve a class of fractional differential equations of order α∈(0,1) in Caputo–Fabrizio sense. Importantly, we highlight relations between the Caputo–Fabrizio and standard first order derivatives that are very important for the understanding of Caputo–Fabrizio theory and how it can be applied. Moreover, using the exactness of differential equations concept, implicit analytical solutions of such equations are presented which are extensions and generalizations to the results found in the literature. Application to fractional order RC type circuits and other examples are given to illustrate the validity and reliability of our results and theory.