Modeling anomalous transport in fractal porous media: A study of fractional diffusion PDEs using numerical method

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Abstract: Fractional diffusion partial differential equation (PDE) models are used to describe anomalous transport phenomena in fractal porous media, where traditional diffusion models may not be applicable due to the presence of long-range dependencies and non-local behaviors. This study presents an efficient hybrid meshless method to the compute numerical solution of a two-dimensional multiterm time-fractional convection-diffusion equation. The proposed meshless method employs multiquadric-cubic radial basis functions for the spatial derivatives, and the Liouville-Caputo derivative technique is used for the time derivative portion of the model equation. The accuracy of the method is evaluated using error norms, and a comparison is made with the exact solution. The numerical results demonstrate that the suggested approach achieves better accuracy and computationally efficient performance.

Location: Deutsche Nationalbibliothek Frankfurt am Main

Extent: Online-Ressource

Language: Englisch

Bibliographic citation: Modeling anomalous transport in fractal porous media: A study of fractional diffusion PDEs using numerical method ; volume:13 ; number:1 ; year:2024 ; extent:11
Nonlinear engineering ; 13, Heft 1 (2024) (gesamt 11)

Creator: Ahmad, Imtiaz
Mekawy, Ibrahim
Khan, Muhammad Nawaz
Jan, Rashid
Boulaaras, Salah

DOI: 10.1515/nleng-2022-0366

URN: urn:nbn:de:101:1-2024031314351908236800

Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.

Last update: 14.08.2025, 10:52 AM CEST

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Ahmad, Imtiaz
Mekawy, Ibrahim
Khan, Muhammad Nawaz
Jan, Rashid
Boulaaras, Salah

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Modeling anomalous transport in fractal porous media: A study of fractional diffusion PDEs using numerical method

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