2025 Volume 15 Issue 2
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Muhammad Nasir, Shuobing Yang, Mohammad Alqudah, Ali M. Mahnashi, Rasool Shah. APPROXIMATE SOLUTION OF FRACTIONAL-ORDER FITZHUGH-NAGUMO EQUATION WITH IN NATURAL TRANSFORM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 624-639. doi: 10.11948/20220410
Citation: Muhammad Nasir, Shuobing Yang, Mohammad Alqudah, Ali M. Mahnashi, Rasool Shah. APPROXIMATE SOLUTION OF FRACTIONAL-ORDER FITZHUGH-NAGUMO EQUATION WITH IN NATURAL TRANSFORM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 624-639. doi: 10.11948/20220410
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APPROXIMATE SOLUTION OF FRACTIONAL-ORDER FITZHUGH-NAGUMO EQUATION WITH IN NATURAL TRANSFORM

  • 1.

    School of mathematical Sciences, Beihang University, Beijing 100191, China

  • 2.

    Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, Jordan

  • 3.

    Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi Arabia

  • 4.

    Department of Mathematics, Abdul Wali Khan University Mardan, Pakistan

    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.

    MSC: 33B15, 34A34, 35A20, 35A22, 44A10
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