A Comparative Analysis of the Non-linear Time Fractional Whitham-Broer-Kaup Equations under Aboodh Decomposition Transform

Authors

  • Ilhem Kadri Department of Mathematics, University of Oran 1 Ahmed Ben Bella, Oran, Algeria https://orcid.org/0000-0002-5719-5297
  • Hami Gundogdu Department of Mathematics, Sakarya University, Serdivan, Turkey
  • Yousif M. Modawy Department of Mathematics, Al-Baha University, Al-Aqiq, Saudi Arabia
  • Ayman Imam Department of Mathematics, Al-Baha University, Al-Aqiq, Saudi Arabia
  • Khadeeja A. A. Helal Department of Mathematics, Faculty of Science , Al-Baha University, P.O. Box 1988, Al Bahah 65799, Saudi Arabia
  • Ibrahim Elshamy Department of Mathematics, Al-Baha University, Al-Aqiq, Saudi Arabia
  • Ranya A. Tahir Department of Mathematics, Jazan University, Jazan, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6626

Keywords:

System of time fractional PDEs, Fractional Whitham-Broer-Kaup equations, Aboodh Transform, Adomian decomposition method, Caputo operator, Atangana-Baleanu-Caputo operator, Caputo-Fabrizio operator

Abstract

This article offers a comprehensive analysis of nonlinear time fractional Whitham-Broer-Kaup equations under Aboodh Decomposition Transform (ADT). The study model examines the effect of different fractional derivative operators on the solution behavior of these equations by comparing them with accuracy, calculation efficiency, and physical lecturer. By employing the Aboodh Transform, a mathematical tool that is powerful in solving fractional differential equations by implementing the Adomian decomposition method, we derive an approximate solutions for models assessed for specific values of the fractional order; the solutions obtained are shown in 2D and 3D. In addition, comparative analyses are performed to clarify the effect of various fractional derivative operators on the solutions achieved, which shows the accuracy and efficiency of ADT in the handling of these complex non-linear fractional partial differential equations. Furthermore, the exact and approximate solutions are compared to the constructed problem to identify the absolute errors.

Downloads

Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Differential Equations

License

Copyright (c) 2025 Ilhem Kadri, Hami Gundogdu, Yousif M. Modawy, Ayman Imam, Khadeeja A. A. Helal, Ibrahim Elshamy, Ranya A. Tahir

Creative Commons License

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

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

A Comparative Analysis of the Non-linear Time Fractional Whitham-Broer-Kaup Equations under Aboodh Decomposition Transform. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6626. https://doi.org/10.29020/nybg.ejpam.v18i3.6626