Analytical solutions of advective–dispersive transport in porous media involving conformable derivative

The advection–dispersion model (ADE) is proposed for an accurate description of fluid flow and solute transport in porous media via the conformable derivative. Analytical solutions of the proposed conformable advection–dispersion equation (CADE) are obtained subject to various initial and boundary conditions. The analytical solutions of CADE in each case are reduced into the classical ADE with the conformable derivative order α=1. Furthermore, compared with the classical ADE, the applicability of the presented CADE models is also validated on the basis of experimental data in literatures.