Citation
Atangana, Abdon and Kilicman, Adem
(2013)
Analytical solutions of the space-time fractional derivative of advection dispersion equation.
Mathematical Problems in Engineering, 2013.
art. no. 853127.
pp. 1-9.
ISSN 1024-123X; ESSN: 1563-5147
Abstract
Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in porous medium. A space-time fractional advection-dispersion equation (FADE) is a generalization of the classical ADE in which the first-order space derivative is replaced with Caputo or Riemann-Liouville derivative of order 0 < β ≤ 1, and the second-order space derivative is replaced with the Caputo or the Riemann-Liouville fractional derivative of order 1 < ≤ 2. We derive the solution of the new equation in terms of Mittag-Leffler functions using Laplace transfrom. Some examples are given. The results from comparison let no doubt that the FADE is better in prediction than ADE.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.1155/2013/853127 |
| Publisher: | Hindawi Publishing Corporation |
| Keywords: | Fractional differential equations; Advection-dispersion equation; Fractional derivatives; Ground-water hydrology; Mittag-Leffler functions; Passive tracers; Riemann-Liouville derivatives; Riemann-Liouville fractional derivatives |
| Depositing User: | Umikalthom Abdullah |
| Date Deposited: | 02 Jul 2014 02:28 |
| Last Modified: | 31 Mar 2016 08:30 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/853127 |
| URI: | http://psasir.upm.edu.my/id/eprint/30133 |
| Statistic Details: | View Download Statistic |
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