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

Abstract and Applied Analysis - Tập 2013 - Trang 1-7 - 2013
Dumitru Bǎleanu1,2,3, Mohsen Alipour4, Hossein Jafari5
1Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Cankaya University, Ogretmenler Cad. 14, Balgat, 06530 Ankara, Turkey
3Institute of Space Sciences, P.O. Box MG 23, Magurele, 077125 Bucharest, Romania
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

Tóm tắt

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.

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Abstract and Applied Analysis

Tập 2013

1-7

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