A reliable numerical algorithm for fractional advection–dispersion equation arising in contaminant transport through porous media

Abstract This article presents a reliable numerical approach for the fractional advection–dispersion equation by making use of Legendre scaling functions as a basis. The fractional advection–dispersion equation describes the anomalous transport in surface and subsurface water. Using two dimensional basis formed by Legendre scaling functions, we get operational matrix for fractional integrations and differentiations. Substituting these operational matrices in the equation leads linear algebraic equations whose solutions can be derived with the aid of Sylvester’s approach; this in turn yields approximate solutions for advection–dispersion equation. Convergence analysis of the proposed scheme is presented. The potency and accuracy of the proposed numerical algorithm are shown by plotting error figures.