Utilization of Adomain Decomposition Method and Laplace Transform to Study Fractional KdV and Fractional Benjamin Models via Caputo Fractional Operator

Authors

Muhammad Sohail, Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, PakistanFollow
Hina Younis, Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, PakistanFollow

Corresponding Author

Muhammad Sohail

Document Type

Research Article

Subject Areas

Applied Mathematics and Computations; Numerical Analysis and Differential Equations

Keywords

Adomian Decomposition method, Caputo Fractional operator, Fractional Benjamin equation, Fractional KdV equation, Laplace transform.

Abstract

In the present study, we implement Adomian decomposition method (ADM) to solve fractional potential Korteweg-de Vries (p-KdV) and Benjamin models. The investigated approach is a hybrid of the Adomian decomposition method and the Laplace transform, and the fractional operator developed by Caputo has been utilized in the present research. In a vast accessible domain, the proposed solution tackle impacts and regulates the gained conclusions. Additionally, it provides a simple technique for determining the point of convergence region of the derived result. To ensure that the LADM is realistic and dependable, mathematical simulations for each equation were run, and the results are shown in tables and graphs. The comparison of the generated answers to the precise solutions demonstrates that the proposed technique is effective in addressing nonlinear problems. The non- linear PDE Korteweg de Vries (KDV) and Benjamin Equations plays an important role in studying waves produced on surface of water and their solution leads to solitons. In this paper, we computed approximate solutions of aforementioned equations by using Laplace Adomain decomposition method. To ensure that the LADM is realistic and dependable, mathematical simulations for each equation were run, and the results are shown in tables and graphs. In a vast accessible domain, the proposed solution tackles impacts and regulates the gained conclusions. The comparison of the generated answers to the exact solutions demonstrates that the proposed technique is effective in addressing nonlinear problems.

How to Cite This Article

Sohail, Muhammad and Younis, Hina (2024) "Utilization of Adomain Decomposition Method and Laplace Transform to Study Fractional KdV and Fractional Benjamin Models via Caputo Fractional Operator," International Journal of Emerging Multidisciplinaries: Mathematics: Vol. 3: Iss. 1, Article 1.
DOI: https://doi.org/10.59790/2790-3257.1044

Receive Date

08-12-2023

Accept Date

01-04-2024

Publication Date

1-14-2024