Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein PolynomialsReport as inadecuate

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The Scientific World Journal - Volume 2014 2014, Article ID 257484, 7 pages -

Research Article

Department of Mathematics, University of Malakand, Dir Lower, Khyber Pakhtunkhwa 18000, Pakistan

Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa 18000, Pakistan

Department of Mathematical Sciences, University of South Africa, P.O. Box 392, UNISA 0003, South Africa

Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

Received 28 July 2014; Revised 2 September 2014; Accepted 2 September 2014; Published 17 November 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Hasib Khan 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.


In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.

Author: Hasib Khan, Hossein Jafari, Rahmat Ali Khan, Haleh Tajadodi, and Sarah Jane Johnston



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