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

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.