The Time-Fractional Coupled-Korteweg-de-Vries Equations
We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The f...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/947986 |
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| _version_ | 1832558172761489408 |
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| author | Abdon Atangana Aydin Secer |
| author_facet | Abdon Atangana Aydin Secer |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| description | We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM). |
| format | Article |
| id | doaj-art-536d0e3830be4b9da762cf53059c15ad |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-536d0e3830be4b9da762cf53059c15ad2025-02-03T01:32:58ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/947986947986The Time-Fractional Coupled-Korteweg-de-Vries EquationsAbdon Atangana0Aydin Secer1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaDepartment of Mathematical Engineering, Yildiz Technical University, Davutpasa, 34210 Istanbul, TurkeyWe put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).http://dx.doi.org/10.1155/2013/947986 |
| spellingShingle | Abdon Atangana Aydin Secer The Time-Fractional Coupled-Korteweg-de-Vries Equations Abstract and Applied Analysis |
| title | The Time-Fractional Coupled-Korteweg-de-Vries Equations |
| title_full | The Time-Fractional Coupled-Korteweg-de-Vries Equations |
| title_fullStr | The Time-Fractional Coupled-Korteweg-de-Vries Equations |
| title_full_unstemmed | The Time-Fractional Coupled-Korteweg-de-Vries Equations |
| title_short | The Time-Fractional Coupled-Korteweg-de-Vries Equations |
| title_sort | time fractional coupled korteweg de vries equations |
| url | http://dx.doi.org/10.1155/2013/947986 |
| work_keys_str_mv | AT abdonatangana thetimefractionalcoupledkortewegdevriesequations AT aydinsecer thetimefractionalcoupledkortewegdevriesequations AT abdonatangana timefractionalcoupledkortewegdevriesequations AT aydinsecer timefractionalcoupledkortewegdevriesequations |