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

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 nonlinea...

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Autores principales: Khan, Hasib, Jafari, Hossein, Khan, Rahmat Ali, Tajadodi, Haleh, Johnston, Sarah Jane
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4251784/
https://www.ncbi.nlm.nih.gov/pubmed/25485293
http://dx.doi.org/10.1155/2014/257484
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author Khan, Hasib
Jafari, Hossein
Khan, Rahmat Ali
Tajadodi, Haleh
Johnston, Sarah Jane
author_facet Khan, Hasib
Jafari, Hossein
Khan, Rahmat Ali
Tajadodi, Haleh
Johnston, Sarah Jane
author_sort Khan, Hasib
collection PubMed
description 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.
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spelling pubmed-42517842014-12-07 Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials Khan, Hasib Jafari, Hossein Khan, Rahmat Ali Tajadodi, Haleh Johnston, Sarah Jane ScientificWorldJournal Research Article 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. Hindawi Publishing Corporation 2014 2014-11-17 /pmc/articles/PMC4251784/ /pubmed/25485293 http://dx.doi.org/10.1155/2014/257484 Text en Copyright © 2014 Hasib Khan et al. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Khan, Hasib
Jafari, Hossein
Khan, Rahmat Ali
Tajadodi, Haleh
Johnston, Sarah Jane
Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
title Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
title_full Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
title_fullStr Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
title_full_unstemmed Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
title_short Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
title_sort numerical solutions of the nonlinear fractional-order brusselator system by bernstein polynomials
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4251784/
https://www.ncbi.nlm.nih.gov/pubmed/25485293
http://dx.doi.org/10.1155/2014/257484
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