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

• Main Authors: Ahmad I., Mekawy I., Khan M.N., Jan R., Boulaaras S.
• Other Authors: 57220824630
• Format: Article
• Published: Walter de Gruyter GmbH 2025
• Subjects: Diffusion in liquids; Fractals; Heat conduction; Heat convection; Image segmentation; Partial differential equations; Porous materials; Radial basis function networks; Base function; Convection-diffusion models; Fractional derivatives; Hybrid multiquadric-cubic radial base function; Meshless collocation methods; Modeling equations; Multi terms; Multiquadrics; Multiterm time-fractional convection-diffusion model equation; Radial basis; Numerical methods

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. ? 2024 the author(s), published by De Gruyter.