Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods
This paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/3/152 |
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| author | Asad Freihat Mohammed Alabedalhadi Shrideh Al-Omari Sharifah E. Alhazmi Shaher Momani Mohammed Al-Smadi |
| author_facet | Asad Freihat Mohammed Alabedalhadi Shrideh Al-Omari Sharifah E. Alhazmi Shaher Momani Mohammed Al-Smadi |
| author_sort | Asad Freihat |
| collection | DOAJ |
| description | This paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlinear ion acoustic waves and thus helping us to understand wave dynamics in plasmas. We introduce a new approach that relies on a new fractional expansion in the natural transform space and residual power series method to construct analytical solutions to the governing models. We investigate the theoretical analysis of the proposed method for these equations to expose this approach’s applicability, efficiency, and effectiveness in constructing analytical solutions to the governing equations. Moreover, we present a comparative discussion between the solutions derived during the work and those given in the literature to confirm that the proposed approach generates analytical solutions that rapidly converge to exact solutions, which proves the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-108e2a54a04343be84c0ee174cca6dcd |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-108e2a54a04343be84c0ee174cca6dcd2025-08-20T02:11:09ZengMDPI AGFractal and Fractional2504-31102025-02-019315210.3390/fractalfract9030152Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series MethodsAsad Freihat0Mohammed Alabedalhadi1Shrideh Al-Omari2Sharifah E. Alhazmi3Shaher Momani4Mohammed Al-Smadi5Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanDepartment of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanDepartment of Mathematics, College of Education for Girls at Al-Qunfudah, Umm Al-Qura University, Mecca 11942, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jordan, Amman 11942, JordanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanThis paper studies three time-fractional models that arise in plasma physics: the modified Korteweg–deVries–Zakharov–Kuznetsov equation, the stochastic potential Korteweg–deVries equation, and the forced Korteweg–deVries equation. These equations are significant in plasma physics for modeling nonlinear ion acoustic waves and thus helping us to understand wave dynamics in plasmas. We introduce a new approach that relies on a new fractional expansion in the natural transform space and residual power series method to construct analytical solutions to the governing models. We investigate the theoretical analysis of the proposed method for these equations to expose this approach’s applicability, efficiency, and effectiveness in constructing analytical solutions to the governing equations. Moreover, we present a comparative discussion between the solutions derived during the work and those given in the literature to confirm that the proposed approach generates analytical solutions that rapidly converge to exact solutions, which proves the effectiveness of the proposed method.https://www.mdpi.com/2504-3110/9/3/152fractional modelplasma physicsKorteweg–deVries equationnatural transformresidual power series method |
| spellingShingle | Asad Freihat Mohammed Alabedalhadi Shrideh Al-Omari Sharifah E. Alhazmi Shaher Momani Mohammed Al-Smadi Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods Fractal and Fractional fractional model plasma physics Korteweg–deVries equation natural transform residual power series method |
| title | Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods |
| title_full | Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods |
| title_fullStr | Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods |
| title_full_unstemmed | Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods |
| title_short | Certain Analytic Solutions for Time-Fractional Models Arising in Plasma Physics via a New Approach Using the Natural Transform and the Residual Power Series Methods |
| title_sort | certain analytic solutions for time fractional models arising in plasma physics via a new approach using the natural transform and the residual power series methods |
| topic | fractional model plasma physics Korteweg–deVries equation natural transform residual power series method |
| url | https://www.mdpi.com/2504-3110/9/3/152 |
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