A Trigonometric Approach to Time Fractional FitzHugh-Nagumo Model on Nerve Pulse Propagation

Abstract

The aim of this paper is to put on display the numerical solutions and dynamics of time fractional Fitzhugh-Nagumo model, which is an important nonlinear reaction-diffusion equation. For this purpose, finite element method based on trigonometric cubic B-splines are used to obtain numerical solutions of the model. In this model, the derivative which is fractional order is taken in terms of Caputo. Thus, time dicretization is made using L1 algorithm for Caputo derivative and space discretization is made using trigonometric cubic B-spline basis. Also, the non-linear term in the model is linearized by the Rubin Graves type linearization. The error norms are calculated for measuring the accuracy of the finite element method. The comparison of numerical and exact solutions are exhibited via tables and graphics.

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

“…Sinan Deniz utilized the optimal perturbation iteration method to derive solutions for the FN equation utilizing AB time-fractional derivatives (9) . Additionally, INan B., Ali K.K., Saha A., and Ak T applied the exponential finite difference method (10) , and Berat Karaagac discussed the finite element method (11) . Alam, M., Haq S., Ali I., and Ebadi M.J. employed radial basis functions (12) .…”