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

Meenakshi Dhumal; Bhausaheb Sontakke

doi:10.17485/IJST/v17i13.3009

Article

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

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i13.3009

Year: 2024, Volume: 17, Issue: 13, Pages: 1272-1282

Original Article

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

Meenakshi Dhumal¹, Bhausaheb Sontakke^2*

¹Department of Mathematics, Deogiri College, Aurangabad, Maharashtra, India
²Department of Mathematics, Pratishthan College, Paithan. Dist., Aurangabad, 431107, Maharashtra, India

*Corresponding Author
Email: [email protected]

Received Date:25 November 2023, Accepted Date:26 February 2024, Published Date:21 March 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: This study aims to explore solutions to the time-fractional Fitzhugh-Nagumo equation, a nonlinear reaction-diffusion equation. Method: We utilize the Homotopy Perturbation Method (HPM) as a proficient analytical approach for addressing the time-fractional Fitzhugh-Nagumo equation. The HPM offers a structured method for deriving approximate solutions in the shape of convergent series, enabling accurate solutions even for intricate nonlinear fractional equations. Finding: The series solution obtained is validated by comparing it with numerical methods, showcasing its precision and effectiveness. Additionally, we assessed the error across various time and space values. Our analysis and computations reveal that the Homotopy Perturbation Method (HPM) stands out for providing precise approximations while maintaining computational efficiency. It's clear that this method presents a robust alternative to conventional numerical techniques, particularly in situations where analytical solutions are difficult to obtain. Novelty: The application of the Homotopy Perturbation Method to the Time-fractional Fitzhugh-Nagumo Equation has been effectively explored, with specific examples showing a strong agreement between the exact solution and the obtained solution.

Keywords: Time-Fractional Fitzhugh–Nagumo Equation, Homotopy Perturbation Method, Riemann-Liouville fractional integral, Caputo fractional derivative, Fractional Homotopy Perturbation Method

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Copyright

© 2024 Dhumal & Sontakke. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)