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<p>The Laplace Adomian Decomposition Method (LADM) and the Laplace Variational Iteration Method (LVIM) are employed in this paper to analytically and numerically solve linear and nonlinear space–time fractional Fokker–Planck equations (STFFPEs). These methods yield analytical solutions in the form of rapidly convergent series without requiring linearization, discretization, perturbation techniques, or restrictive assumptions. The proposed approaches are simple to implement, computationally efficient, and highly reliable. Several STFFPEs are solved using the proposed methods, and the solutions are presented both numerically and graphically, alongside comparisons with exact solutions to verify their accuracy, effectiveness, and stability. Furthermore, the numerical results of LADM and LVIM are compared with those obtained by existing techniques, demonstrating superior performance in terms of accuracy and reliability. In addition, the stability, convergence, and error analysis of the proposed methods for nonlinear STFFPEs are carried out to confirm their effectiveness.</p>

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Laplace Adomian decomposition method and Laplace variational iteration method approaches to the nonlinear space-time fractional Fokker-Planck equation

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Monowar Hossain,
  • Mohammed Aman Ullah

摘要

The Laplace Adomian Decomposition Method (LADM) and the Laplace Variational Iteration Method (LVIM) are employed in this paper to analytically and numerically solve linear and nonlinear space–time fractional Fokker–Planck equations (STFFPEs). These methods yield analytical solutions in the form of rapidly convergent series without requiring linearization, discretization, perturbation techniques, or restrictive assumptions. The proposed approaches are simple to implement, computationally efficient, and highly reliable. Several STFFPEs are solved using the proposed methods, and the solutions are presented both numerically and graphically, alongside comparisons with exact solutions to verify their accuracy, effectiveness, and stability. Furthermore, the numerical results of LADM and LVIM are compared with those obtained by existing techniques, demonstrating superior performance in terms of accuracy and reliability. In addition, the stability, convergence, and error analysis of the proposed methods for nonlinear STFFPEs are carried out to confirm their effectiveness.