Existence of solutions for Nonlinear Caputo-Fabrizio fractional differential equations

Abstract

We examine the solution to a nonlinear fractional differential equation in this research work that involves the Caputo-Fabrizio fractional derivatives. We extend our analysis to the Caputo-Fabrizio fractional derivative in a coupled system of nonlinear fractional differential equations. We use the Banach
contraction principle, Schauder's fixed point theorem, and Babenko's approach to get the intended results. Furthermore, we provide the required conditions and inequalities, based on the Lipschitz hypothesis, to show that solutions to our problem exist and are unique. We provide three instances to further support our primary findings.