Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation
The Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice. In this article, the generalized exp(-Φ(ξ))-expansion metho...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/6743276 |
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| author | Dianchen Lu Chen Yue Muhammad Arshad |
| author_facet | Dianchen Lu Chen Yue Muhammad Arshad |
| author_sort | Dianchen Lu |
| collection | DOAJ |
| description | The Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice. In this article, the generalized exp(-Φ(ξ))-expansion method is proposed to construct exact solutions of space-time fractional generalized fifth-order KdV equation with Jumarie’s modified Riemann-Liouville derivatives. At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations. |
| format | Article |
| id | doaj-art-f4f27ad392ef4a49b455bd260b7ddc90 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f4f27ad392ef4a49b455bd260b7ddc902025-02-03T00:59:01ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/67432766743276Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV EquationDianchen Lu0Chen Yue1Muhammad Arshad2Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, ChinaDepartment of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, ChinaDepartment of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, ChinaThe Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice. In this article, the generalized exp(-Φ(ξ))-expansion method is proposed to construct exact solutions of space-time fractional generalized fifth-order KdV equation with Jumarie’s modified Riemann-Liouville derivatives. At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.http://dx.doi.org/10.1155/2017/6743276 |
| spellingShingle | Dianchen Lu Chen Yue Muhammad Arshad Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation Advances in Mathematical Physics |
| title | Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation |
| title_full | Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation |
| title_fullStr | Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation |
| title_full_unstemmed | Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation |
| title_short | Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation |
| title_sort | traveling wave solutions of space time fractional generalized fifth order kdv equation |
| url | http://dx.doi.org/10.1155/2017/6743276 |
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