Work

Numerical simulation of the generalized FitzHugh–Nagumo equation by employing the fractional Newton explicit group algorithm

Year: 2025

Type: article

Abstract: In this research, the Fractional Newton Explicit Group Method (FNEGM) is used as an accurate and efficient method to provide a numerical simulation of the Caputo time-Fractional Generalized FitzHugh–Nagumo Equation (FGFNE). The implicit Finite Difference Method (FDM) is applied to approximate the fractional derivative operator, which in turn transforms the equation into a system of algebraic equations that is solved utilizing the modified Newton method. Some studies are cited to discuss the convergence and stability of the proposed method. The method is evaluated in terms of its efficiency and convergence rate by solving some systems and comparing the solutions obtained tabularly or graphically at several orders of fractional derivatives. The parameters in the equation are also evaluated to demonstrate their influence on the behavior of the solutions. The application of this method demonstrates its effectiveness in solving this type of real-world issues.

Source: Alexandria Engineering Journal

DOI: 10.1016/j.aej.2025.10.014

Authors: M.M. Khader, A. Alaidrous, M. Adel

Institutions: Imam Mohammad ibn Saud Islamic University, Umm al-Qura University, Islamic University of Madinah

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,900

Funders: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University, Imam Mohammed Ibn Saud Islamic University