| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2022-0410 |
| Approximate solution of fractional-order Fitzhugh-Nagumo Equation with in Natural transform |
| A. A. Alderremy,Imran Khan,Shaban Aly,Muhammed Naeem,Rasool Shah |
| Keywords:Natural iterative transform method Natural residual power series method Fitzhugh- Nagumo equation Fractional order differential equation Caputo operator. |
| Abstract: |
| In this paper, we use, for the first time, the Natural residual power series method (NRPSM) as a new
iteration method to study the Caputo version of the Fitzhugh-Nagumo equation. The Fitzhugh-Nagumo
equation is an essential mathematical model that is widely used to characterize the behavior of excitable
systems, and is valuable for understanding significant physiological and biological processes. To start,
we translate the Fitzhugh-Nagumo equation system into its Natural domain representation, and then we
employ the NRPSM to obtain a series form result. After that, we present a new iteration methodology for
improving the convergence characteristics of the series solution as well as the accuracy of the computations.
In this paper, a comprehensive approach for investigating the Fitzhugh-Nagumo equation with Natural
transform is developed and validated, thus can help researchers to explore the various dynamics and
behaviors of the excitable systems more effectively. Based on the results obtained, we conclude that the
suggested approach to the solution of DEs with the Caputo operator has a great potential for different
applications in several fields of science and engineering. |
PDF Download reader
|
|
|
|