Exploring fractional dynamics in the FitzHugh-Nagumo model with the Caputo operator

• Published in: Boundary value problems Vol. 2025; no. 1; pp. 127 - 20
• Main Authors: Almusawa, Musawa Yahya, Aldawsari, Khalid, Mshary, Noorah
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 28.08.2025; Hindawi Limited; SpringerOpen
• Subjects: Accuracy; Analysis; Applications; Applications of mathematics; Approximations and Expansions; Calculus; Caputo operator; Difference and Functional Equations; Exact solutions; Fitzhugh-Nagumo equation; Mathematics; Mathematics and Statistics; Methods; Mohand residual power series method (MRPSM); Mohand transform iterative method (MTIM); Nonlinear differential equations; Numerical analysis; Ordinary Differential Equations; Partial Differential Equations; Power series; Recent Advances in Nonlinear Elliptic Partial Differential Equations: Theory; Time fractional partial differential equation; Mohand residual power series method (MRPSM); Mohand transform iterative method (MTIM); Time fractional partial differential equation; Caputo operator; Fitzhugh-Nagumo equation
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-025-02115-6

In this paper, we study the fractional FitzHugh-Nagumo (FHN) equation which is a standard model for excitable systems; particularly nerve impulse propagation. We used the Mohand Iterative Transform Method (MTIM) and Mohand Residual Power Series Transform Method (MRPSM) to obtain approximate analytical solutions of the equation related to Caputo sense fractional order differential equations. The aim of these methods is to tackle the complications brought about by the fractional derivatives, enabling an efficient study of the behavior of the system. This work validates the effectiveness and reliability of the MTIM and MRPSM by comparing them with each other and with exact solutions. The study delivers significant contributions in unraveling the behaviour of fractional-order systems and serves as a platform for future studies in nonlinear differential equations from the realm of applied mathematics and computational physics.