title: Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Malakand, Dir Lower, Khyber Pakhtunkhwa 18000, Pakistan ; Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa 18000, Pakistan.
authors.forename: Hasib
authors.identifier: 0000-0002-7186-8435
authors.initials: H
authors.lastname: Khan
authors.affiliation: Department of Mathematical Sciences, University of South Africa, P.O. Box 392, UNISA 0003, South Africa.
authors.forename: Hossein
authors.identifier: 0000-0001-6807-6675
authors.initials: H
authors.lastname: Jafari
authors.affiliation: Department of Mathematics, University of Malakand, Dir Lower, Khyber Pakhtunkhwa 18000, Pakistan.
authors.forename: Rahmat Ali
authors.initials: RA
authors.lastname: Khan
authors.affiliation: Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran.
authors.forename: Haleh
authors.initials: H
authors.lastname: Tajadodi
authors.affiliation: Department of Mathematical Sciences, University of South Africa, P.O. Box 392, UNISA 0003, South Africa.
authors.forename: Sarah Jane
authors.initials: SJ
authors.lastname: Johnston
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008433:Mathematics; D008962:Models, Theoretical