Homotopy Perturbation Method For Fractional Shallow Water Equations
In this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis met...
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| Format: | Article |
| Language: | English |
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Sultan Qaboos University
2014-06-01
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| Series: | Sultan Qaboos University Journal for Science |
| Subjects: | |
| Online Access: | https://journals.squ.edu.om/index.php/squjs/article/view/423 |
| _version_ | 1819060528454041600 |
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| author | Kamel Al-Khaled M. K. Al-Safeen |
| author_facet | Kamel Al-Khaled M. K. Al-Safeen |
| author_sort | Kamel Al-Khaled |
| collection | DOAJ |
| description | In this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis method, to solve certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. The results obtained reveal that these methods are both very effective and simple for finding approximate solutions. Some numerical examples and plots are presented to illustrate the efficiency and reliability of these methods. |
| first_indexed | 2024-12-21T14:28:25Z |
| format | Article |
| id | doaj.art-f9d7324bf54e448d873951ac30a7e3ff |
| institution | Directory Open Access Journal |
| issn | 1027-524X 2414-536X |
| language | English |
| last_indexed | 2024-12-21T14:28:25Z |
| publishDate | 2014-06-01 |
| publisher | Sultan Qaboos University |
| record_format | Article |
| series | Sultan Qaboos University Journal for Science |
| spelling | doaj.art-f9d7324bf54e448d873951ac30a7e3ff2022-12-21T19:00:34ZengSultan Qaboos UniversitySultan Qaboos University Journal for Science1027-524X2414-536X2014-06-01191748610.24200/squjs.vol19iss1pp74-86418Homotopy Perturbation Method For Fractional Shallow Water EquationsKamel Al-Khaled0M. K. Al-Safeen1Department of Mathematics and Statistics, Sultan Qaboos University, Box: 36, Al-Khoudh 123, Muscat, Sultanate of Oman2Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, JordanIn this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis method, to solve certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. The results obtained reveal that these methods are both very effective and simple for finding approximate solutions. Some numerical examples and plots are presented to illustrate the efficiency and reliability of these methods.https://journals.squ.edu.om/index.php/squjs/article/view/423Homotopy perturbation, Fractional differential equation, Shallow water equations, Approximate solutions. |
| spellingShingle | Kamel Al-Khaled M. K. Al-Safeen Homotopy Perturbation Method For Fractional Shallow Water Equations Sultan Qaboos University Journal for Science Homotopy perturbation, Fractional differential equation, Shallow water equations, Approximate solutions. |
| title | Homotopy Perturbation Method For Fractional Shallow Water Equations |
| title_full | Homotopy Perturbation Method For Fractional Shallow Water Equations |
| title_fullStr | Homotopy Perturbation Method For Fractional Shallow Water Equations |
| title_full_unstemmed | Homotopy Perturbation Method For Fractional Shallow Water Equations |
| title_short | Homotopy Perturbation Method For Fractional Shallow Water Equations |
| title_sort | homotopy perturbation method for fractional shallow water equations |
| topic | Homotopy perturbation, Fractional differential equation, Shallow water equations, Approximate solutions. |
| url | https://journals.squ.edu.om/index.php/squjs/article/view/423 |
| work_keys_str_mv | AT kamelalkhaled homotopyperturbationmethodforfractionalshallowwaterequations AT mkalsafeen homotopyperturbationmethodforfractionalshallowwaterequations |