A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation
The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/498381 |
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| author | Abdon Atangana S. C. Oukouomi Noutchie |
| author_facet | Abdon Atangana S. C. Oukouomi Noutchie |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| description | The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer) in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method. |
| format | Article |
| id | doaj-art-05e867582c554895be80d9ac92b43fd5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-05e867582c554895be80d9ac92b43fd52025-02-03T06:11:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/498381498381A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives ApproximationAbdon Atangana0S. C. Oukouomi Noutchie1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaDepartment of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South AfricaThe notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer) in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.http://dx.doi.org/10.1155/2014/498381 |
| spellingShingle | Abdon Atangana S. C. Oukouomi Noutchie A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation Abstract and Applied Analysis |
| title | A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation |
| title_full | A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation |
| title_fullStr | A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation |
| title_full_unstemmed | A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation |
| title_short | A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation |
| title_sort | modified groundwater flow model using the space time riemann liouville fractional derivatives approximation |
| url | http://dx.doi.org/10.1155/2014/498381 |
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