Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform
In this paper, the Elzaki transform decomposition method is implemented to solve the time-fractional Swift–Hohenberg equations. The presented model is related to the temperature and thermal convection of fluid dynamics, which can also be used to explain the formation process in liquid surfaces bound...
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| Format: | Article |
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MDPI AG
2021-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/7/1263 |
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| author | Kamsing Nonlaopon Abdullah M. Alsharif Ahmed M. Zidan Adnan Khan Yasser S. Hamed Rasool Shah |
| author_facet | Kamsing Nonlaopon Abdullah M. Alsharif Ahmed M. Zidan Adnan Khan Yasser S. Hamed Rasool Shah |
| author_sort | Kamsing Nonlaopon |
| collection | DOAJ |
| description | In this paper, the Elzaki transform decomposition method is implemented to solve the time-fractional Swift–Hohenberg equations. The presented model is related to the temperature and thermal convection of fluid dynamics, which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In the Caputo manner, the fractional derivative is described. The suggested method is easy to implement and needs a small number of calculations. The validity of the presented method is confirmed from the numerical examples. Illustrative figures are used to derive and verify the supporting analytical schemes for fractional-order of the proposed problems. It has been confirmed that the proposed method can be easily extended for the solution of other linear and non-linear fractional-order partial differential equations. |
| first_indexed | 2024-03-10T09:22:10Z |
| format | Article |
| id | doaj.art-ccef003323c64050bd566b11f77e752d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T09:22:10Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ccef003323c64050bd566b11f77e752d2023-11-22T05:09:44ZengMDPI AGSymmetry2073-89942021-07-01137126310.3390/sym13071263Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel TransformKamsing Nonlaopon0Abdullah M. Alsharif1Ahmed M. Zidan2Adnan Khan3Yasser S. Hamed4Rasool Shah5Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Abdul Wali University Mardan, Mardan 23200, PakistanDepartment of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics, Abdul Wali University Mardan, Mardan 23200, PakistanIn this paper, the Elzaki transform decomposition method is implemented to solve the time-fractional Swift–Hohenberg equations. The presented model is related to the temperature and thermal convection of fluid dynamics, which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In the Caputo manner, the fractional derivative is described. The suggested method is easy to implement and needs a small number of calculations. The validity of the presented method is confirmed from the numerical examples. Illustrative figures are used to derive and verify the supporting analytical schemes for fractional-order of the proposed problems. It has been confirmed that the proposed method can be easily extended for the solution of other linear and non-linear fractional-order partial differential equations.https://www.mdpi.com/2073-8994/13/7/1263Elzaki transformationAdomian decomposition methodtime-fractional Swift–Hohenberg equationCaputo operator |
| spellingShingle | Kamsing Nonlaopon Abdullah M. Alsharif Ahmed M. Zidan Adnan Khan Yasser S. Hamed Rasool Shah Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform Symmetry Elzaki transformation Adomian decomposition method time-fractional Swift–Hohenberg equation Caputo operator |
| title | Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform |
| title_full | Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform |
| title_fullStr | Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform |
| title_full_unstemmed | Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform |
| title_short | Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform |
| title_sort | numerical investigation of fractional order swift hohenberg equations via a novel transform |
| topic | Elzaki transformation Adomian decomposition method time-fractional Swift–Hohenberg equation Caputo operator |
| url | https://www.mdpi.com/2073-8994/13/7/1263 |
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