Document Type

Article

Source of Publication

International Journal of Differential Equations

Publication Date

11-18-2024

Abstract

This paper leverages the Bernstein operational matrices method for the first time in order to resolve the nonlinear fractional smoking epidemic model presented in terms of Caputo’s fractional derivative. An approximate solution is derived using Bernstein’s operational matrices and strategically chosen collocation points. This is followed by the validation of the proposed method’s accuracy and reliability against the established Runge–Kutta fourth‐order method. Furthermore, a comprehensive comparative analysis is conducted against two prominent techniques: the fractional differential transform method (FDTM) and the q‐homotopy analysis transform method (q‐HATM). The results show a superior and significant performance regarding accuracy as well as approximation. A residual corrected error technique is employed to enhance the precision of the presented method, thus effectively minimising absolute errors.

ISSN

1687-9651

Publisher

Wiley

Volume

2024

Issue

1

Disciplines

Mathematics

Keywords

Bernstein operational matrices, fractional-order model, smoking epidemic, Caputo’s fractional derivative, residual corrected error

Creative Commons License

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

Indexed in Scopus

no

Open Access

yes

Open Access Type

Gold: This publication is openly available in an open access journal/series

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Included in

Mathematics Commons

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