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 |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30133/1/30133.pdf |
| _version_ | 1825947647122341888 |
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| author | Atangana, Abdon Kilicman, Adem |
| author_facet | Atangana, Abdon Kilicman, Adem |
| author_sort | Atangana, Abdon |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T08:16:35Z |
| format | Article |
| id | upm.eprints-30133 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:16:35Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-301332016-03-31T08:30:18Z http://psasir.upm.edu.my/id/eprint/30133/ Analytical solutions of the space-time fractional derivative of advection dispersion equation Atangana, Abdon Kilicman, Adem 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. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30133/1/30133.pdf 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 http://www.hindawi.com/journals/mpe/2013/853127/abs/ 10.1155/2013/853127 |
| spellingShingle | Atangana, Abdon Kilicman, Adem Analytical solutions of the space-time fractional derivative of advection dispersion equation |
| title | Analytical solutions of the space-time fractional derivative of advection dispersion equation |
| title_full | Analytical solutions of the space-time fractional derivative of advection dispersion equation |
| title_fullStr | Analytical solutions of the space-time fractional derivative of advection dispersion equation |
| title_full_unstemmed | Analytical solutions of the space-time fractional derivative of advection dispersion equation |
| title_short | Analytical solutions of the space-time fractional derivative of advection dispersion equation |
| title_sort | analytical solutions of the space time fractional derivative of advection dispersion equation |
| url | http://psasir.upm.edu.my/id/eprint/30133/1/30133.pdf |
| work_keys_str_mv | AT atanganaabdon analyticalsolutionsofthespacetimefractionalderivativeofadvectiondispersionequation AT kilicmanadem analyticalsolutionsofthespacetimefractionalderivativeofadvectiondispersionequation |