Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method
The article examines the fractional stochastic Korteweg-de Vries (FSKdV) equation, with a focus on space-time white noise and conformable fractional derivatives (CFD). The primary aim is to utilize the generalized Riccati equation mapping (GREM) method to derive soliton and soliton-like, periodic an...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Tamkang University Press
2025-06-01
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| Series: | Journal of Applied Science and Engineering |
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| Online Access: | http://jase.tku.edu.tw/articles/jase-202603-29-03-0002 |
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| author | Abaker A. Hassaballa Ali Satty Mohyaldein Salih Ahmed M. A. Adam Omer M. A. Hamed Zakariya M. S. Mohammed Ashraf F. A. Mahmoud Elzain A. E. Gumma |
| author_facet | Abaker A. Hassaballa Ali Satty Mohyaldein Salih Ahmed M. A. Adam Omer M. A. Hamed Zakariya M. S. Mohammed Ashraf F. A. Mahmoud Elzain A. E. Gumma |
| author_sort | Abaker A. Hassaballa |
| collection | DOAJ |
| description | The article examines the fractional stochastic Korteweg-de Vries (FSKdV) equation, with a focus on space-time white noise and conformable fractional derivatives (CFD). The primary aim is to utilize the generalized Riccati equation mapping (GREM) method to derive soliton and soliton-like, periodic and rational solutions for the FSKdV equation, taking into account various conditions of space-time fractional order beside white noise as well. The acquired exact analytical solutions’ physical characteristics are elucidated through graphical illustrations,
which clearly show the effects of changing the fractional order and including the stochastic term. The results confirm the GREM method’s reliability and effectiveness in solving the FSKdV equation. |
| format | Article |
| id | doaj-art-a0c1e72019bb4bfd89234333ec0990b2 |
| institution | OA Journals |
| issn | 2708-9967 2708-9975 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Tamkang University Press |
| record_format | Article |
| series | Journal of Applied Science and Engineering |
| spelling | doaj-art-a0c1e72019bb4bfd89234333ec0990b22025-08-20T02:34:56ZengTamkang University PressJournal of Applied Science and Engineering2708-99672708-99752025-06-0129351151910.6180/jase.202603_29(3).0002Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping MethodAbaker A. Hassaballa0Ali Satty1Mohyaldein Salih2Ahmed M. A. Adam3Omer M. A. Hamed4Zakariya M. S. Mohammed5Ashraf F. A. Mahmoud6Elzain A. E. Gumma7Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, Saudi Arabia. Department of Mathematics, College of Science, Northern Border University, Arar, Saud ArabiaDepartment of Mathematics, College of Science, Northern Border University, Arar, Saud ArabiaDepartment of Mathematics, College of Science, Northern Border University, Arar, Saud ArabiaDepartment of Mathematics, College of Science, Northern Border University, Arar, Saud ArabiaDepartment of Finance, College of Business Administration, Northern Border University, Arar, Saudi ArabiaCenter for Scientific Research and Entrepreneurship, Northern Border University, Arar, Saudi Arabia. Department of Mathematics, College of Science, Northern Border University, Arar, Saud ArabiaTranslation, Authorship and Publication Center, Northern Border University, Arar, Saudi Arabia. Department of Computer Science, College of Science, Northern Border University, Arar, Saudi ArabiaDepartment of Mathematics, College of Science, Northern Border University, Arar, Saud ArabiaThe article examines the fractional stochastic Korteweg-de Vries (FSKdV) equation, with a focus on space-time white noise and conformable fractional derivatives (CFD). The primary aim is to utilize the generalized Riccati equation mapping (GREM) method to derive soliton and soliton-like, periodic and rational solutions for the FSKdV equation, taking into account various conditions of space-time fractional order beside white noise as well. The acquired exact analytical solutions’ physical characteristics are elucidated through graphical illustrations, which clearly show the effects of changing the fractional order and including the stochastic term. The results confirm the GREM method’s reliability and effectiveness in solving the FSKdV equation.http://jase.tku.edu.tw/articles/jase-202603-29-03-0002generalizing riccati equation mapping methodconformable fractional derivativesfractional stochastic korteweg-de vries equationnonlinear partial differential equation |
| spellingShingle | Abaker A. Hassaballa Ali Satty Mohyaldein Salih Ahmed M. A. Adam Omer M. A. Hamed Zakariya M. S. Mohammed Ashraf F. A. Mahmoud Elzain A. E. Gumma Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method Journal of Applied Science and Engineering generalizing riccati equation mapping method conformable fractional derivatives fractional stochastic korteweg-de vries equation nonlinear partial differential equation |
| title | Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method |
| title_full | Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method |
| title_fullStr | Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method |
| title_full_unstemmed | Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method |
| title_short | Analytical Solutions for the Nonlinear Stochastic Fractional KdV Equation: An application of the Generalized Riccati Equation Mapping Method |
| title_sort | analytical solutions for the nonlinear stochastic fractional kdv equation an application of the generalized riccati equation mapping method |
| topic | generalizing riccati equation mapping method conformable fractional derivatives fractional stochastic korteweg-de vries equation nonlinear partial differential equation |
| url | http://jase.tku.edu.tw/articles/jase-202603-29-03-0002 |
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