Solving Nonlinear Fractional Differential Equations by Bernstein Polynomials Operational Matrices


Authors

Mohsen Alipour - Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran. Davood Rostamy - Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran.


Abstract

In this paper, we solve nonlinear fractional differential equations by Bernstein polynomials. Firstly, we derive the Bernstein polynomials (BPs) operational matrix for the fractional derivative in the Caputo sense, which has not been undertaken before. This method reduces the problems to a system of algebraic equations. The results obtained are in good agreement with the analytical solutions and the numerical solutions in open literatures. Also, the solutions approach to classical solutions as the order of the fractional derivatives approach to 1.


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ISRP Style

Mohsen Alipour, Davood Rostamy, Solving Nonlinear Fractional Differential Equations by Bernstein Polynomials Operational Matrices , Journal of Mathematics and Computer Science, 5 (2012), no. 3, 185 - 196

AMA Style

Alipour Mohsen, Rostamy Davood, Solving Nonlinear Fractional Differential Equations by Bernstein Polynomials Operational Matrices . J Math Comput SCI-JM. (2012); 5(3):185 - 196

Chicago/Turabian Style

Alipour, Mohsen, Rostamy, Davood. "Solving Nonlinear Fractional Differential Equations by Bernstein Polynomials Operational Matrices ." Journal of Mathematics and Computer Science, 5, no. 3 (2012): 185 - 196


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