The Caputo-Fabrizio fractional derivative applied to a singular perturbation problem

Abstract

The garden equation is a nonlinear partial differential equation that has application in more than two different fields. In this paper, we use the Caputo-Fabrizio derivative with fractional order to extend this model to the concept of fractional calculus. In the process, we prove that the new derivative satisfies the equality of mixed partial and in the extended equation, we present the analysis of existence and uniqueness of the exact solution. We propose a special solution using the Laplace iterative methods. Some numerical simulations are preformed for different values of alpha and also the perturbed parameter.