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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34669/ http://psasir.upm.edu.my/id/eprint/34669/1/Note%20on%20the%20Convergence%20Analysis%20of%20Homotopy%20Perturbation.pdf |
| _version_ | 1848847838167957504 |
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| author | Elbeleze, Asma Ali Kilicman, Adem M. Taib, Bachok |
| author_facet | Elbeleze, Asma Ali Kilicman, Adem M. Taib, Bachok |
| author_sort | Elbeleze, Asma Ali |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T09:24:58Z |
| format | Article |
| id | upm-34669 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:24:58Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-346692017-10-19T07:47:13Z http://psasir.upm.edu.my/id/eprint/34669/ Note on the convergence analysis of homotopy perturbation method for fractional partial differential equations Elbeleze, Asma Ali Kilicman, Adem M. Taib, Bachok 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. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/34669/1/Note%20on%20the%20Convergence%20Analysis%20of%20Homotopy%20Perturbation.pdf Elbeleze, Asma Ali and Kilicman, Adem and M. Taib, Bachok (2014) Note on the convergence analysis of homotopy perturbation method for fractional partial differential equations. Abstract and Applied Analysis, 2014. art. no. 803902. pp. 1-8. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2014/803902/abs/ 10.1155/2014/803902 |
| spellingShingle | Elbeleze, Asma Ali Kilicman, Adem M. Taib, Bachok Note on the convergence analysis of homotopy perturbation method for fractional partial differential equations |
| 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://psasir.upm.edu.my/id/eprint/34669/ http://psasir.upm.edu.my/id/eprint/34669/ http://psasir.upm.edu.my/id/eprint/34669/ http://psasir.upm.edu.my/id/eprint/34669/1/Note%20on%20the%20Convergence%20Analysis%20of%20Homotopy%20Perturbation.pdf |