Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|Number of page(s)
|29 March 2019
Analysis of advective–diffusive transport phenomena modelled via non-singular Mittag-Leffler kernel
Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University,
* Corresponding author: email@example.com
Accepted: 12 February 2019
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.
Mathematics Subject Classification: 35R11 / 26A33 / 65M80 / 35A22
Key words: Atangana–Baleanu derivative / advection–diffusion equation / fundamental solution / Mittag-Leffler / Fourier transform
© EDP Sciences, 2019
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