Numerical treatment of the coupled fractional mKdV equations based on the Adomian decomposition technique

Authors

Jihan Alahmadi, Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al- Kharj, 11942, Saudi ArabiaFollow
Bashayer Aldossary, Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al- Kharj, 11942, Saudi ArabiaFollow
Emad A-B Abdel-Salam, Department of Mathematics, Faculty of Science, New Valley University, El-Kharja 72511, EgyptFollow

Author Country (or Countries)

Saudi Arabia

Abstract

The present research implements the decomposition Adomian approach of the approximation solution for the nonlinear coupled modification Korteweg-De Vries (KdV) model in space time fractional order with appropriate initial values. This method yields a power series calculation for the solution. This process does not require linearization, the concept of weak nonlinear nature assumption, or perturbation theory. A mathematical software like Mathematica or Maple has been used to evaluate the Adomian formulas of the consequent series solution. This procedure might additionally be applied to resolve various types of fractional order nonlinear mathematical physics models. A graphic discussion is provided regarding the behavior of Adomian solutions and the varying changes in non integer order values and their effects. The approach is simple, clear and general enough to be used with other nonlinear fractional problems in mathematics and physics.

Digital Object Identifier (DOI)

https://dx.doi.org/10.18576/amis/180110

Recommended Citation

Alahmadi, Jihan; Aldossary, Bashayer; and A-B Abdel-Salam, Emad (2024) "Numerical treatment of the coupled fractional mKdV equations based on the Adomian decomposition technique," Applied Mathematics & Information Sciences: Vol. 18: Iss. 1, Article 9.
DOI: https://dx.doi.org/10.18576/amis/180110
Available at: https://digitalcommons.aaru.edu.jo/amis/vol18/iss1/9