A generalized kinetic model of the advection-dispersion process in a sorbing medium

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated considering constitutive equation diffusive flux derivative. Analytical solutions determined using Laplace transform method. solution corresponding ordinary compared four models fractional