On the Singular Perturbations for Fractional Differential Equation
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact so...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/752371 |
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doaj-ff2e45a2a471455485f60767f4cb1d062020-11-24T21:49:00ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/752371752371On the Singular Perturbations for Fractional Differential EquationAbdon Atangana0Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South AfricaThe goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.http://dx.doi.org/10.1155/2014/752371 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Abdon Atangana |
| spellingShingle |
Abdon Atangana On the Singular Perturbations for Fractional Differential Equation The Scientific World Journal |
| author_facet |
Abdon Atangana |
| author_sort |
Abdon Atangana |
| title |
On the Singular Perturbations for Fractional Differential Equation |
| title_short |
On the Singular Perturbations for Fractional Differential Equation |
| title_full |
On the Singular Perturbations for Fractional Differential Equation |
| title_fullStr |
On the Singular Perturbations for Fractional Differential Equation |
| title_full_unstemmed |
On the Singular Perturbations for Fractional Differential Equation |
| title_sort |
on the singular perturbations for fractional differential equation |
| publisher |
Hindawi Limited |
| series |
The Scientific World Journal |
| issn |
2356-6140 1537-744X |
| publishDate |
2014-01-01 |
| description |
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. |
| url |
http://dx.doi.org/10.1155/2014/752371 |
| work_keys_str_mv |
AT abdonatangana onthesingularperturbationsforfractionaldifferentialequation |
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1725890040898256896 |