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Analytical solutions of the space-time fractional derivative of advection dispersion equation

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

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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.

Item Type:Article
Keyword:Fractional differential equations; Advection-dispersion equation; Fractional derivatives; Ground-water hydrology; Mittag-Leffler functions; Passive tracers; Riemann-Liouville derivatives; Riemann-Liouville fractional derivatives
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:Hindawi Publishing Corporation
DOI Number:10.1155/2013/853127
Altmetrics:http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/853127
ID Code:30133
Deposited By: Umikalthom Abdullah
Deposited On:02 Jul 2014 10:28
Last Modified:31 Mar 2016 16:30

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