Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in a...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/482419 |
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| author | Khaled A. Gepreel Taher A. Nofal Fawziah M. Alotaibi |
| author_facet | Khaled A. Gepreel Taher A. Nofal Fawziah M. Alotaibi |
| author_sort | Khaled A. Gepreel |
| collection | DOAJ |
| description | We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation. |
| format | Article |
| id | doaj-art-9730aaccdd3c4a999e15e7482db7593c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9730aaccdd3c4a999e15e7482db7593c2025-02-03T01:30:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/482419482419Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential EquationsKhaled A. Gepreel0Taher A. Nofal1Fawziah M. Alotaibi2Mathematics Department, Faculty of Science, Taif University, Taif, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, Taif, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, Taif, Saudi ArabiaWe implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation.http://dx.doi.org/10.1155/2013/482419 |
| spellingShingle | Khaled A. Gepreel Taher A. Nofal Fawziah M. Alotaibi Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations Journal of Applied Mathematics |
| title | Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations |
| title_full | Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations |
| title_fullStr | Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations |
| title_full_unstemmed | Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations |
| title_short | Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations |
| title_sort | numerical solutions for the time and space fractional nonlinear partial differential equations |
| url | http://dx.doi.org/10.1155/2013/482419 |
| work_keys_str_mv | AT khaledagepreel numericalsolutionsforthetimeandspacefractionalnonlinearpartialdifferentialequations AT taheranofal numericalsolutionsforthetimeandspacefractionalnonlinearpartialdifferentialequations AT fawziahmalotaibi numericalsolutionsforthetimeandspacefractionalnonlinearpartialdifferentialequations |