A Collocation Method for Solving Fractional Riccati Differential Equation
We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/598083 |
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| _version_ | 1832556918536667136 |
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| author | Yalçın Öztürk Ayşe Anapalı Mustafa Gülsu Mehmet Sezer |
| author_facet | Yalçın Öztürk Ayşe Anapalı Mustafa Gülsu Mehmet Sezer |
| author_sort | Yalçın Öztürk |
| collection | DOAJ |
| description | We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate. |
| format | Article |
| id | doaj-art-cf347dab5a6a4249adad07fda4f19e2c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-cf347dab5a6a4249adad07fda4f19e2c2025-02-03T05:44:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/598083598083A Collocation Method for Solving Fractional Riccati Differential EquationYalçın Öztürk0Ayşe Anapalı1Mustafa Gülsu2Mehmet Sezer3Ula Ali Koçman Vocational Scholl, Muğla Sıtkı Koçman University, 48000 Muğla, TurkeyDepartment of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000 Muğla, TurkeyDepartment of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000 Muğla, TurkeyDepartment of Mathematics, Faculty of Science and Arts, Celal Bayar University, 45047 Manisa, TurkeyWe have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.http://dx.doi.org/10.1155/2013/598083 |
| spellingShingle | Yalçın Öztürk Ayşe Anapalı Mustafa Gülsu Mehmet Sezer A Collocation Method for Solving Fractional Riccati Differential Equation Journal of Applied Mathematics |
| title | A Collocation Method for Solving Fractional Riccati Differential Equation |
| title_full | A Collocation Method for Solving Fractional Riccati Differential Equation |
| title_fullStr | A Collocation Method for Solving Fractional Riccati Differential Equation |
| title_full_unstemmed | A Collocation Method for Solving Fractional Riccati Differential Equation |
| title_short | A Collocation Method for Solving Fractional Riccati Differential Equation |
| title_sort | collocation method for solving fractional riccati differential equation |
| url | http://dx.doi.org/10.1155/2013/598083 |
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