Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations
We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is pr...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/803902 |
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| _version_ | 1850166979473702912 |
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| author | Asma Ali Elbeleze Adem Kılıçman Bachok M. Taib |
| author_facet | Asma Ali Elbeleze Adem Kılıçman Bachok M. Taib |
| author_sort | Asma Ali Elbeleze |
| collection | DOAJ |
| description | We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many
linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method. |
| format | Article |
| id | doaj-art-e4dfdae2c7b244b18f8606e0510fb2b8 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e4dfdae2c7b244b18f8606e0510fb2b82025-08-20T02:21:18ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/803902803902Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential EquationsAsma Ali Elbeleze0Adem Kılıçman1Bachok M. Taib2Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), 71800 Nilai, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaFaculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), 71800 Nilai, MalaysiaWe apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.http://dx.doi.org/10.1155/2014/803902 |
| spellingShingle | Asma Ali Elbeleze Adem Kılıçman Bachok M. Taib Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations Abstract and Applied Analysis |
| title | Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations |
| title_full | Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations |
| title_fullStr | Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations |
| title_full_unstemmed | Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations |
| title_short | Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations |
| title_sort | note on the convergence analysis of homotopy perturbation method for fractional partial differential equations |
| url | http://dx.doi.org/10.1155/2014/803902 |
| work_keys_str_mv | AT asmaalielbeleze noteontheconvergenceanalysisofhomotopyperturbationmethodforfractionalpartialdifferentialequations AT ademkılıcman noteontheconvergenceanalysisofhomotopyperturbationmethodforfractionalpartialdifferentialequations AT bachokmtaib noteontheconvergenceanalysisofhomotopyperturbationmethodforfractionalpartialdifferentialequations |