Solution of time fractional Fitzhugh–Nagumo equation using semi analytical techniques

Abstract

In this work, we apply three different techniques to solve the Fitzhugh–Nagumo equation that is an important equation used to describe the propagation of electrical signals in excitable media, such as nerve fibers. Residual power series method (RPSM), homotopy perturbation method (HPM), and a modified fractional Taylor expansion, are applied to this nonlinear equation to obtain approximate solutions. By comparing the exact solution with the approximate solutions obtained from the methods suggested we demonstrate that these methods are efficient tools to solve nonlinear fractional partial differential equations (NFPDE) this is due to the high accuracy obtained. To support the current solution investigation, various graphs in 2D and 3D are shown.

Keywords

• Time fractional Fitzhugh–Nagumo equation
• Residual power series method
• Homotopy perturbation method
• Modified fractional Taylor series method
• Caputo fractional derivatives and integrals