Wavelet−ALA fusion scheme for (2+1)D time−fractional mobile/immobile models

A numerical scheme is proposed, merging 3D eighth−kind fractional Chebyshev wavelets with the artificial lemming algorithm (ALA) to address (2+1)D time−fractional mobile/immobile models. Initially, we construct the 3D eighth−kind fractional Chebyshev wavelets and investigate their properties, including approximation capability and convergence analysis. Furthermore, by establishing a multivariate Caputo fractional Taylor formula, error bounds for the presented wavelets approximation are derived. Then, we provide a detailed algorithmic procedure for solving the (2+1)D time−fractional mobile/immobile models considered in this paper, incorporating the ALA. Finally, the performance of the proposed method is examined through selected numerical examples. Comparative studies with existing findings provide quantitative evidence of the method's accuracy and the enhanced computational efficiency resulting from ALA incorporation. Moreover, our method remains applicable to 3D space−fractional differential equations, and we validate this claim through a 3D space−fractional Poisson equation.