Semi-Analytical Solution of the Fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) System via the Laplace Transform Adomian Decomposition Method

Sarita Pippal

doi:10.62762/JNSPM.2026.197265

Article Information

Published in Journal of Numerical Simulations in Physics and Mathematics

Volume/Issue Volume 2, Issue 1, 2026

Pages 59-68

Abstract

This study explores the application of the Adomian Decomposition Method (ADM), combined with the Laplace transform, to obtain approximate solutions of the time--fractional Wazwaz--Benjamin--Bona--Mahony (WBBM) equations. These equations, which describe wave phenomena in fluid dynamics within a fractional--time framework, present significant analytical challenges. By integrating the Laplace transform with ADM, a modified technique---referred to as the Laplace Transform Adomian Decomposition Method (LTADM)---is introduced. The time--fractional WBBM equations are solved using LTADM, and three--dimensional solution plots are generated for six different values of the fractional order \( \delta \) (0.5, 0.6, 0.7, 0.8, 0.9, and 1). The results demonstrate that LTADM is an efficient and reliable method for solving nonlinear fractional differential equations such as the WBBM model.

Graphical Abstract

Semi-Analytical Solution of the Fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) System via the Laplace Transform Adomian Decomposition Method

Keywords

fractional calculus laplace transform adomian decomposition method WBBM system nonlinear evolution equations

Data Availability Statement

Data will be made available on request.

Funding

This work was supported without any funding.

Conflicts of Interest

The authors declare no conflicts of interest.

AI Use Statement

The authors declare that generative AI was used in the preparation of this manuscript, limited to language refinement. The AI tool employed was ChatGPT-5. No AI was used for data analysis, result interpretation, conceptual development, or generation of core scientific content. The authors take full responsibility for the accuracy, originality, and integrity of the work.

Ethical Approval and Consent to Participate

Not applicable.

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APA Style

Pippal, S. (2026). Semi-Analytical Solution of the Fractional Wazwaz--Benjamin--Bona--Mahony (WBBM) System via the Laplace Transform Adomian Decomposition Method. Journal of Numerical Simulations in Physics and Mathematics, 2(1), 59-68. https://doi.org/10.62762/JNSPM.2026.197265

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TY  - JOUR
AU  - Pippal, Sarita
PY  - 2026
DA  - 2026/05/28
TI  - Semi-Analytical Solution of the Fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) System via the Laplace Transform Adomian Decomposition Method
JO  - Journal of Numerical Simulations in Physics and Mathematics
T2  - Journal of Numerical Simulations in Physics and Mathematics
JF  - Journal of Numerical Simulations in Physics and Mathematics
VL  - 2
IS  - 1
SP  - 59
EP  - 68
DO  - 10.62762/JNSPM.2026.197265
UR  - https://www.icck.org/article/abs/JNSPM.2026.197265
KW  - fractional calculus
KW  - laplace transform
KW  - adomian decomposition method
KW  - WBBM system
KW  - nonlinear evolution equations
AB  - This study explores the application of the Adomian Decomposition Method (ADM), combined with the Laplace transform, to obtain approximate solutions of the time--fractional Wazwaz--Benjamin--Bona--Mahony (WBBM) equations. These equations, which describe wave phenomena in fluid dynamics within a fractional--time framework, present significant analytical challenges. By integrating the Laplace transform with ADM, a modified technique---referred to as the Laplace Transform Adomian Decomposition Method (LTADM)---is introduced. The time--fractional WBBM equations are solved using LTADM, and three--dimensional solution plots are generated for six different values of the fractional order \( \delta \) (0.5, 0.6, 0.7, 0.8, 0.9, and 1). The results demonstrate that LTADM is an efficient and reliable method for solving nonlinear fractional differential equations such as the WBBM model.
SN  - 3068-9082
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -

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@article{Pippal2026SemiAnalyt,
  author = {Sarita Pippal},
  title = {Semi-Analytical Solution of the Fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) System via the Laplace Transform Adomian Decomposition Method},
  journal = {Journal of Numerical Simulations in Physics and Mathematics},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {59-68},
  doi = {10.62762/JNSPM.2026.197265},
  url = {https://www.icck.org/article/abs/JNSPM.2026.197265},
  abstract = {This study explores the application of the Adomian Decomposition Method (ADM), combined with the Laplace transform, to obtain approximate solutions of the time--fractional Wazwaz--Benjamin--Bona--Mahony (WBBM) equations. These equations, which describe wave phenomena in fluid dynamics within a fractional--time framework, present significant analytical challenges. By integrating the Laplace transform with ADM, a modified technique---referred to as the Laplace Transform Adomian Decomposition Method (LTADM)---is introduced. The time--fractional WBBM equations are solved using LTADM, and three--dimensional solution plots are generated for six different values of the fractional order \( \delta \) (0.5, 0.6, 0.7, 0.8, 0.9, and 1). The results demonstrate that LTADM is an efficient and reliable method for solving nonlinear fractional differential equations such as the WBBM model.},
  keywords = {fractional calculus, laplace transform, adomian decomposition method, WBBM system, nonlinear evolution equations},
  issn = {3068-9082},
  publisher = {Institute of Central Computation and Knowledge}
}

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