Global solution to a nonlinear fractional differential equation for the Caputo-Fabrizio derivative

Abstract

In this article we prove existence and uniqueness of global solution to an initial value problem for a nonlinear fractional differential equation with a Caputo-Fabrizio (CF) derivative. We provide a new compact formula for the computation of the CF derivative to power functions (which is given in terms of Mittag-Leffler functions). We also give the convergence to classical derivatives for a regular class of functions when the order of the CF derivative tends to one, as well as some other useful properties.