Solving Time-Fractional Fitzhugh–Nagumo Equation using Homotopy Perturbation Method

Abstract

Objectives: This study aims to explore solutions to the time-fractional Fitzhugh-Nagumo equation, a nonlinear reaction-diffusion equation. Method: We utilize the Homotopy Perturbation Method (HPM) as a proficient analytical approach for addressing the time-fractional Fitzhugh-Nagumo equation. The HPM offers a structured method for deriving approximate solutions in the shape of convergent series, enabling accurate solutions even for intricate nonlinear fractional equations. Finding: The series solution obtained is validated by comparing it with numerical methods, showcasing its precision and effectiveness. Additionally, we assessed the error across various time and space values. Our analysis and computations reveal that the Homotopy Perturbation Method (HPM) stands out for providing precise approximations while maintaining computational efficiency. It's clear that this method presents a robust alternative to conventional numerical techniques, particularly in situations where analytical solutions are difficult to obtain. Novelty: The application of the Homotopy Perturbation Method to the Time-fractional Fitzhugh-Nagumo Equation has been effectively explored, with specific examples showing a strong agreement between the exact solution and the obtained solution. Keywords: Time-Fractional Fitzhugh–Nagumo Equation, Homotopy Perturbation Method, Riemann-Liouville fractional integral, Caputo fractional derivative, Fractional Homotopy Perturbation Method