### Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

Hasib Khan, Hossein Jafari, Rahmat Ali Khan, Haleh Tajadodi, Sarah Jane Johnston
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nxzqpsogkbe55mjq33syzghf2e" style="color: black;">The Scientific World Journal</a> </i> &nbsp;
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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/257484">doi:10.1155/2014/257484</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/25485293">pmid:25485293</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC4251784/">pmcid:PMC4251784</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ei53selkpfbdhobnkclwnmlotm">fatcat:ei53selkpfbdhobnkclwnmlotm</a> </span>
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