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Journal of Applied Mathematics
Volume 2013, Article ID 598083, 8 pages
Research Article

A Collocation Method for Solving Fractional Riccati Differential Equation

1Ula Ali Koçman Vocational Scholl, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey
2Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey
3Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, 45047 Manisa, Turkey

Received 29 March 2013; Accepted 9 July 2013

Academic Editor: Jafar Biazar

Copyright © 2013 Yalçın Öztürk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.