Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations
In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can ea...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2014-12-01
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| Series: | Baghdad Science Journal |
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| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2060 |
| _version_ | 1818662852006772736 |
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| author | Baghdad Science Journal |
| author_facet | Baghdad Science Journal |
| author_sort | Baghdad Science Journal |
| collection | DOAJ |
| description | In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations. |
| first_indexed | 2024-12-17T05:07:32Z |
| format | Article |
| id | doaj.art-821d4cf1b4d2455a8ff5ca3d032b1010 |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-12-17T05:07:32Z |
| publishDate | 2014-12-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-821d4cf1b4d2455a8ff5ca3d032b10102022-12-21T22:02:22ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862014-12-0111410.21123/bsj.11.4.1637-1648Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential EquationsBaghdad Science JournalIn this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2060Homotopy perturbation method, fractional calculas, integro-differential equations. |
| spellingShingle | Baghdad Science Journal Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations Baghdad Science Journal Homotopy perturbation method, fractional calculas, integro-differential equations. |
| title | Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations |
| title_full | Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations |
| title_fullStr | Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations |
| title_full_unstemmed | Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations |
| title_short | Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations |
| title_sort | convergence of the generalized homotopy perturbation method for solving fractional order integro differential equations |
| topic | Homotopy perturbation method, fractional calculas, integro-differential equations. |
| url | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2060 |
| work_keys_str_mv | AT baghdadsciencejournal convergenceofthegeneralizedhomotopyperturbationmethodforsolvingfractionalorderintegrodifferentialequations |