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Advances in Mathematical Physics
Volume 2013, Article ID 954015, 9 pages
Research Article

Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

1Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran
2Department of Mathematics and Computer Sciences, Cankaya University, 06530 Ankara, Turkey
3Institute of Space Sciences, P.O. Box MG-23, 077125 Magurele-Bucharest, Romania
4Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Received 20 February 2013; Revised 6 March 2013; Accepted 7 March 2013

Academic Editor: José Tenreiro Machado

Copyright © 2013 Mohsen Alipour and Dumitru Baleanu. 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 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.