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<p>This paper presents a new conjunction technique called Khalouta decomposition method (KHDM) for solving systems of nonlinear fractional partial differential equations. The technique we consider is the combination of the Khalouta transform in the sense of the Atangana-Baleanu-Caputo fractional derivative and a new decomposition method which was developed in Khalouta (Sahand Commun. Math. Anal 21(3):165–196, 2024). The uniqueness and convergence of the solutions are proven using Banach’s fixed point theorem. The advantage of using KHDM is that it gives a more accurate convergence series to the exact solution and requires only a small computational size without involving perturbation, discretization, or any other restrictive physical conditions. Three numerical applications are presented to verify the validity of the main results. In addition, the results of this study are graphically illustrated using the mathematical software Matlab, and the solution graphs demonstrate that the approximate solution is closely related to the exact solution. The obtained results confirm the effectiveness of this new technique for treating complex nonlinear systems involving fractional derivatives.</p>

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A novel conjunction technique for systems of nonlinear fractional partial differential equations under Khalouta-Atangana-Baleanu-Caputo fractional derivative

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Ali Khalouta

摘要

This paper presents a new conjunction technique called Khalouta decomposition method (KHDM) for solving systems of nonlinear fractional partial differential equations. The technique we consider is the combination of the Khalouta transform in the sense of the Atangana-Baleanu-Caputo fractional derivative and a new decomposition method which was developed in Khalouta (Sahand Commun. Math. Anal 21(3):165–196, 2024). The uniqueness and convergence of the solutions are proven using Banach’s fixed point theorem. The advantage of using KHDM is that it gives a more accurate convergence series to the exact solution and requires only a small computational size without involving perturbation, discretization, or any other restrictive physical conditions. Three numerical applications are presented to verify the validity of the main results. In addition, the results of this study are graphically illustrated using the mathematical software Matlab, and the solution graphs demonstrate that the approximate solution is closely related to the exact solution. The obtained results confirm the effectiveness of this new technique for treating complex nonlinear systems involving fractional derivatives.