Analysis of advective–diffusive transport phenomena modelled via non-singular Mittag-Leffler kernel

Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University, 10145 Çağış, Balıkesir, Turkey.

^* Corresponding author: dkaradeniz@balikesir.edu.tr

Received: 26 September 2018
Accepted: 12 February 2019

Abstract

In this study, a linear advection–diffusion equation described by Atangana–Baleanu derivative with non-singular Mittag-Leffler kernel is considered. The Cauchy, Dirichlet and source problems are formulated on the half-line. The main motivation of this work is to find the fundamental solutions of prescribed problems. For this purpose, Laplace transform method with respect to time t and sine/cosine-Fourier transform methods with respect to spatial coordinate x are applied. It is remarkable that the obtained results are quite similar to the existing fundamental solutions of advection–diffusion equation with time-Caputo fractional derivative. Although the results are mathematically similar in both formulations, the AB derivative is a non-singular operator and provides a significant advantage in the computational processes. Therefore, it is preferable to replace the Caputo derivative in modelling such diffusive transports.