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
Official URL: http://www.hindawi.com/journals/mpe/2013/853127/ab...
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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