Numerical solution for generalized Fitzhugh-Nagumo equations by variational iteration transform method

Abstract

This study applies the variational iteration transform method (VITM) to obtain analytical solutions of the generalized fractional-order FitzHugh–Nagumo equation with a singular kernel derivative, which models the dynamics of excitable cells such as neurons and cardiac cells. The method combines variational iteration techniques with the Shehu transform, along with established tools from fractional calculus, including the Riemann–Liouville fractional integral and Caputo fractional derivative. Solutions are constructed using successive applications of the Shehu transform and its inverse. The convergence and uniqueness of the proposed method are rigorously analyzed. The accuracy and efficiency of VITM are validated through comparisons with exact solutions and existing methods for various fractional orders $\mu$. The results demonstrate that the proposed approach is simple, reliable, and highly accurate for solving nonlinear fractional differential equations.