Analytical and numerical study of a nonlinear Volterra integro-differential equation with the Caputo-Fabrizio fractional derivative

Abstract

In this paper we interest concerns an integro-differential equation of Volterra when the derivative of the solution appears under the sign of integration in a non-linear way. The derivation is the Caputo-Fabrizio Fractional Derivative (CF-FD), which increases the interest of this study. we built Lipchitz conditions to obtain the existence and uniqueness of the solution in a Banach space specific to the derivative of Caputo. The analytical study is followed by a complete numerical study.