Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative
The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional der...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/8819183 |
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| author | Majid Bagheri Ali Khani |
| author_facet | Majid Bagheri Ali Khani |
| author_sort | Majid Bagheri |
| collection | DOAJ |
| description | The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena. |
| format | Article |
| id | doaj-art-6de8f84df0af4e1f80e4f5ab63e2285b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-6de8f84df0af4e1f80e4f5ab63e2285b2025-08-20T03:33:50ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/88191838819183Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional DerivativeMajid Bagheri0Ali Khani1Faculty of Science, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranFaculty of Science, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranThe present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena.http://dx.doi.org/10.1155/2020/8819183 |
| spellingShingle | Majid Bagheri Ali Khani Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative Advances in Mathematical Physics |
| title | Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative |
| title_full | Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative |
| title_fullStr | Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative |
| title_full_unstemmed | Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative |
| title_short | Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative |
| title_sort | analytical method for solving the fractional order generalized kdv equation by a beta fractional derivative |
| url | http://dx.doi.org/10.1155/2020/8819183 |
| work_keys_str_mv | AT majidbagheri analyticalmethodforsolvingthefractionalordergeneralizedkdvequationbyabetafractionalderivative AT alikhani analyticalmethodforsolvingthefractionalordergeneralizedkdvequationbyabetafractionalderivative |