The New Travelling Wave Solutions of Time Fractional Fitzhugh-Nagumo Equation with Sine-Gordon Expansion Method

Abstract

Authors aimed to employ the sine-Gordon expansion method to acquire the new exact solutions of fractional Fitzhugh-Nagumo equation which is a stripped type of the Hodgkin-Huxley model that expresses in extensive way activation and deactivation dynamics of neuron spiking. By using the wave transformations, by the practicality of chain rule and applicability of the conformable fractional derivative, the fractional nonlinear partial differential equation (FNPDE) changes to a nonlinear ordinary differential equation. So the exact solution of the considered equation can be obtained correctly with the aid of efficient and reliable analytical techniques. Keywords: Sine-Gordon expansion method; Fitzhugh-Nagumo Equation; Conformable derivative.