The Extended Trial Equation Method for Some Time Fractional Differential Equations
Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be t...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/491359 |
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| _version_ | 1832553234412077056 |
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| author | Yusuf Pandir Yusuf Gurefe Emine Misirli |
| author_facet | Yusuf Pandir Yusuf Gurefe Emine Misirli |
| author_sort | Yusuf Pandir |
| collection | DOAJ |
| description | Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractional Kn,n equation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions. |
| format | Article |
| id | doaj-art-fa48c98d50084eb0b2dff1143c4d8530 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fa48c98d50084eb0b2dff1143c4d85302025-02-03T05:55:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/491359491359The Extended Trial Equation Method for Some Time Fractional Differential EquationsYusuf Pandir0Yusuf Gurefe1Emine Misirli2Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, TurkeyDepartment of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, TurkeyDepartment of Mathematics, Faculty of Science, Ege University, 35100 Izmir, TurkeyNonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractional Kn,n equation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions.http://dx.doi.org/10.1155/2013/491359 |
| spellingShingle | Yusuf Pandir Yusuf Gurefe Emine Misirli The Extended Trial Equation Method for Some Time Fractional Differential Equations Discrete Dynamics in Nature and Society |
| title | The Extended Trial Equation Method for Some Time Fractional Differential Equations |
| title_full | The Extended Trial Equation Method for Some Time Fractional Differential Equations |
| title_fullStr | The Extended Trial Equation Method for Some Time Fractional Differential Equations |
| title_full_unstemmed | The Extended Trial Equation Method for Some Time Fractional Differential Equations |
| title_short | The Extended Trial Equation Method for Some Time Fractional Differential Equations |
| title_sort | extended trial equation method for some time fractional differential equations |
| url | http://dx.doi.org/10.1155/2013/491359 |
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