A homotopy-based computational scheme for two-dimensional fractional cable equation

Title

A homotopy-based computational scheme for two-dimensional fractional cable equation

Creator

Kumar C.V.D.; Prakasha D.G.; Veeresha P.; Kapoor M.

Description

In this paper, we examine the time-dependent two-dimensional cable equation of fractional order in terms of the Caputo fractional derivative. This cable equation plays a vital role in diverse areas of electrophysiology and modeling neuronal dynamics. This paper conveys a precise semi-analytical method called the q-homotopy analysis transform method to solve the fractional cable equation. The proposed method is based on the conjunction of the q-homotopy analysis method and Laplace transform. We explained the uniqueness of the solution produced by the suggested method with the help of Banach's fixed-point theory. The results obtained through the considered method are in the form of a series solution, and they converge rapidly. The obtained outcomes were in good agreement with the exact solution and are discussed through the 3D plots and graphs that express the physical representation of the considered equation. It shows that the proposed technique used here is reliable, well-organized and effective in analyzing the considered non-homogeneous fractional differential equations arising in various branches of science and engineering. 2024 World Scientific Publishing Company.

Source

Modern Physics Letters B, Vol-38, No. 32

Date

2024-01-01

Publisher

World Scientific

Subject

Caputo derivative; Fractional cable equation; Laplace transform; q -homotopy analysis transform method

Coverage

Kumar C.V.D., Department of Mathematics, Davangere University, Shivagangotri, Davangere, 577007, India; Prakasha D.G., Department of Mathematics, Davangere University, Shivagangotri, Davangere, 577007, India; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru, 560029, India; Kapoor M., Department of Mathematics, Lovely Professional University, Punjab, Phagwara, 144411, India

Rights

Restricted Access

Relation

ISSN: 2179849; CODEN: MPLBE

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S0217984924502920

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