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

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.

Automated summary

In this work, three different techniques are applied to solve the Fitzhugh-Nagumo equation, which is important for describing the propagation of electrical signals in excitable media. The methods used, including the residual power series method, homotopy perturbation method, and a modified fractional Taylor expansion, provide accurate solutions for nonlinear fractional partial differential equations. The comparison between exact and approximate solutions demonstrates the efficiency and high accuracy of these methods. Various 2D and 3D graphs are shown to support the analysis.