Analytical solutions of the space-time fractional derivative of advection dispersion equation
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 derivativ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30133/ http://psasir.upm.edu.my/id/eprint/30133/ http://psasir.upm.edu.my/id/eprint/30133/ http://psasir.upm.edu.my/id/eprint/30133/1/30133.pdf |
| Summary: | 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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