Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices
We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, w...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/954015 |
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| author | Mohsen Alipour Dumitru Baleanu |
| author_facet | Mohsen Alipour Dumitru Baleanu |
| author_sort | Mohsen Alipour |
| collection | DOAJ |
| description | We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1. |
| format | Article |
| id | doaj-art-cbe38eee2a84492c968eaba427cbcea2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-cbe38eee2a84492c968eaba427cbcea22025-02-03T01:26:49ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/954015954015Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational MatricesMohsen Alipour0Dumitru Baleanu1Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, IranDepartment of Mathematics and Computer Sciences, Cankaya University, 06530 Ankara, TurkeyWe present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.http://dx.doi.org/10.1155/2013/954015 |
| spellingShingle | Mohsen Alipour Dumitru Baleanu Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices Advances in Mathematical Physics |
| title | Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices |
| title_full | Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices |
| title_fullStr | Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices |
| title_full_unstemmed | Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices |
| title_short | Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices |
| title_sort | approximate analytical solution for nonlinear system of fractional differential equations by bps operational matrices |
| url | http://dx.doi.org/10.1155/2013/954015 |
| work_keys_str_mv | AT mohsenalipour approximateanalyticalsolutionfornonlinearsystemoffractionaldifferentialequationsbybpsoperationalmatrices AT dumitrubaleanu approximateanalyticalsolutionfornonlinearsystemoffractionaldifferentialequationsbybpsoperationalmatrices |