Analytical modelling of fractional advection–dispersion equation defined in a bounded space domain

The fractional advection–dispersion equation (FADE) known as its non-local dispersion, is used in groundwater hydrology and has been proven to be a reliable tool to model the transport of passive tracers carried by fluid flow in a porous media. In this paper, compact structures of FADE are investigated by means of the homotopy perturbation method with consideration of a promising scheme to calculate nonlinear terms. The problems are formulated in the Jumarie sense. Analytical and numerical results are presented.