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

¹ Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania.
² Section of Mathematics, Academy of Romanian Scientists, 050094 Bucharest, Romania.
³ Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
⁴ Department of Mechanical Engineering, Sejong University, Seoul, South Korea.
⁵ Department of Mathematics, Lahore Leads University, Lahore, Pakistan.

^* Corresponding author: nehadali199@yahoo.com

Received: 17 October 2020
Accepted: 10 April 2021

Abstract

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