A popular reaction-diffusion model fractional Fitzhugh-Nagumo equation: analytical and numerical treatment

The main objective of this article is to obtain the new analytical and numerical solutions of fractional Fitzhugh-Nagumo equation which arises as a model of reaction-diffusion systems, transmission of nerve impulses, circuit theory, biology and the area of population genetics. For this aim conformable derivative with fractional order which is a well behaved, understandable and applicable definition is used as a tool. The analytical solutions were got by utilizing the fact that the conformable fractional derivative provided the chain rule. By the help of this feature which is not provided by other popular fractional derivatives, nonlinear fractional partial differential equation is turned into an integer order differential equation. The numerical solutions which is obtained with the aid of residual power series method are compared with the analytical results that obtained by performing sub equation method. This comparison is made both with the help of three-dimensional graphical representations and tables for different values of the γ.