An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations
In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/5234151 |
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| author | Moh’d Khier Al-Srihin Mohammed Al-Refai |
| author_facet | Moh’d Khier Al-Srihin Mohammed Al-Refai |
| author_sort | Moh’d Khier Al-Srihin |
| collection | DOAJ |
| description | In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed. |
| format | Article |
| id | doaj-art-00dae98266d443a4bbd5d2b8859b3b03 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-00dae98266d443a4bbd5d2b8859b3b032025-08-20T02:02:48ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/52341515234151An Efficient Series Solution for Nonlinear Multiterm Fractional Differential EquationsMoh’d Khier Al-Srihin0Mohammed Al-Refai1Department of Mathematical Sciences, United Arab Emirates University, Al-Ain, UAEDepartment of Mathematical Sciences, United Arab Emirates University, Al-Ain, UAEIn this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.http://dx.doi.org/10.1155/2017/5234151 |
| spellingShingle | Moh’d Khier Al-Srihin Mohammed Al-Refai An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations Discrete Dynamics in Nature and Society |
| title | An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations |
| title_full | An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations |
| title_fullStr | An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations |
| title_full_unstemmed | An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations |
| title_short | An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations |
| title_sort | efficient series solution for nonlinear multiterm fractional differential equations |
| url | http://dx.doi.org/10.1155/2017/5234151 |
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