Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform
In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonli...
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MDPI AG
2024-08-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/9/512 |
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| author | Zhihua Chen Saeed Kosari Jana Shafi Mohammad Hossein Derakhshan |
| author_facet | Zhihua Chen Saeed Kosari Jana Shafi Mohammad Hossein Derakhshan |
| author_sort | Zhihua Chen |
| collection | DOAJ |
| description | In this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonlinear terms are handled with the assistance of the homotopy polynomials. The stability analysis of the implemented method is studied by using S-stable mapping and the Banach contraction principle. Also, we use the fixed-point method to determine the existence and uniqueness of solutions in the given suggested model. Finally, some numerical simulations are illustrated to display the accuracy and efficiency of the present numerical method. Moreover, numerical behaviors are captured to validate the reliability and efficiency of the scheme. |
| format | Article |
| id | doaj-art-2fbe9ece2f3f453b8f5fa87e2564804c |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-2fbe9ece2f3f453b8f5fa87e2564804c2025-08-20T01:55:27ZengMDPI AGFractal and Fractional2504-31102024-08-018951210.3390/fractalfract8090512Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik TransformZhihua Chen0Saeed Kosari1Jana Shafi2Mohammad Hossein Derakhshan3Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaInstitute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Computer Engineering and Information, College of Engineering in Wadi Alddawasir, Prince Sattam Bin Abdulaziz University, Wadi Alddawasir 11991, Saudi ArabiaDepartment of Industrial Engineering, Apadana Institute of Higher Education, Shiraz 7187985443, IranIn this manuscript, we survey a numerical algorithm based on the combination of the homotopy perturbation method and the Sadik transform for solving the time-fractional nonlinear modified shallow water waves (called Kawahara equation) within the frame of the Caputo–Prabhakar (CP) operator. The nonlinear terms are handled with the assistance of the homotopy polynomials. The stability analysis of the implemented method is studied by using S-stable mapping and the Banach contraction principle. Also, we use the fixed-point method to determine the existence and uniqueness of solutions in the given suggested model. Finally, some numerical simulations are illustrated to display the accuracy and efficiency of the present numerical method. Moreover, numerical behaviors are captured to validate the reliability and efficiency of the scheme.https://www.mdpi.com/2504-3110/8/9/512homotopy perturbation transform methodmodified Kawahara equationSadik transform methodCaputo–Prabhakar fractional derivative |
| spellingShingle | Zhihua Chen Saeed Kosari Jana Shafi Mohammad Hossein Derakhshan Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform Fractal and Fractional homotopy perturbation transform method modified Kawahara equation Sadik transform method Caputo–Prabhakar fractional derivative |
| title | Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform |
| title_full | Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform |
| title_fullStr | Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform |
| title_full_unstemmed | Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform |
| title_short | Stability Analysis Study of Time-Fractional Nonlinear Modified Kawahara Equation Based on the Homotopy Perturbation Sadik Transform |
| title_sort | stability analysis study of time fractional nonlinear modified kawahara equation based on the homotopy perturbation sadik transform |
| topic | homotopy perturbation transform method modified Kawahara equation Sadik transform method Caputo–Prabhakar fractional derivative |
| url | https://www.mdpi.com/2504-3110/8/9/512 |
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