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<p>The accurate modeling and analysis of the physical phenomena in systems of high complexity normally demands advanced mathematical methods, in particular when coupled system of the diffusion-reaction type are concerned. These systems are essential in modelling a variety of phenomenon in physics, chemistry, biology, as well as engineering, where interactions among multiple components and spatial-temporal dynamics can be influenced by both the processes of diffusion and the presence of the nonlinear reaction kinetics. This paper examines semi analytical solution of the diffusion-reaction system using Aboodh Residual Power Series Method and Aboodh transform iteration Method within the framework of the Caputo fractional order derivative. The results of the proposed methods are compared and contrasted with the classical variational iteration method. The accuracies, simplicity and convergence emphasise the efficiency of their usefulness to simulate fractional models in science and engineering.</p>

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Solving coupled systems of physical equations with fractional derivatives using Aboodh transform methods

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月30日

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  • Musawa Yahya Almusawa,
  • Khalid Aldawsari,
  • Noorah Mshary

摘要

The accurate modeling and analysis of the physical phenomena in systems of high complexity normally demands advanced mathematical methods, in particular when coupled system of the diffusion-reaction type are concerned. These systems are essential in modelling a variety of phenomenon in physics, chemistry, biology, as well as engineering, where interactions among multiple components and spatial-temporal dynamics can be influenced by both the processes of diffusion and the presence of the nonlinear reaction kinetics. This paper examines semi analytical solution of the diffusion-reaction system using Aboodh Residual Power Series Method and Aboodh transform iteration Method within the framework of the Caputo fractional order derivative. The results of the proposed methods are compared and contrasted with the classical variational iteration method. The accuracies, simplicity and convergence emphasise the efficiency of their usefulness to simulate fractional models in science and engineering.