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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 461970, 7 pages
http://dx.doi.org/10.1155/2013/461970
Research Article

The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative

1Department of Mathematics, Cankaya University, Ogretmenler Cad. 14, Balgat, 06530 Ankara, Turkey
2Institute of Space Sciences, P.O. Box MG 23, Magurele, 077125 Bucharest, Romania
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
4Faculty of Basic Science, Babol University of Technology, P.O. Box 47148-71167, Babol, Iran
5Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

Received 6 April 2013; Accepted 22 May 2013

Academic Editor: Ali H. Bhrawy

Copyright © 2013 Dumitru Baleanu 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.

Abstract

We obtain the approximate analytical solution for the fractional quadratic Riccati differential equation with the Riemann-Liouville derivative by using the Bernstein polynomials (BPs) operational matrices. In this method, we use the operational matrix for fractional integration in the Riemann-Liouville sense. Then by using this matrix and operational matrix of product, we reduce the problem to a system of algebraic equations that can be solved easily. The efficiency and accuracy of the proposed method are illustrated by several examples.