What question did this study set out to answer?

This work aims to validate a new numerical method for solving time-fractional Fokker-Planck equations addressing anomalous diffusion.

April 24, 2026Boundary Value ProblemsOpen Access

Graphical and numerical validation of the least-square Laplace residual power series method for fractional Fokker-Planck equations: a study of anomalous diffusion

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Authors

AAAhmad AlbaityJazan University MAMusaad S. AldhabaniUniversity of Tabuk AHAli H. HakamiJazan University

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Implication

Numerical analysis demonstrates the accuracy of the Laplace residual method for modeling anomalous diffusion, suggesting improvements in computational efficiency.

Key Points

This work aims to validate a new numerical method for solving time-fractional Fokker-Planck equations addressing anomalous diffusion.
Utilized the least-square Laplace residual power series method to derive approximate solutions.
Integrated Laplace transform framework with least-square residual approximation.
Compared results with the iterative transform and homotopy perturbation methods.
The proposed method yielded significantly smaller absolute errors compared to competing methods.
Graphical analysis showed that memory effects play an important role in the dynamics of anomalous diffusion.
Results demonstrate the accuracy and computational efficiency of the least-square Laplace residual power series method.

Cite This Study

Albaity et al. (2026) studied this question.

synapsesocial.com/papers/69eb092b553a5433e34b3bc8 https://doi.org/10.1186/s13661-026-02281-1

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Implication

Numerical analysis demonstrates the accuracy of the Laplace residual method for modeling anomalous diffusion, suggesting improvements in computational efficiency.

Graphical and numerical validation of the least-square Laplace residual power series method for fractional Fokker-Planck equations: a study of anomalous diffusion

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Implication

Key Points

Cite This Study

Graphical and numerical validation of the least-square Laplace residual power series method for fractional Fokker-Planck equations: a study of anomalous diffusion

Discussion

Member takes

Implication

Key Points

Cite This Study

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