Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808810120200521Numerical method for solving a class of two-dimensional fractional optimal control problem of via operational matrices of Legendre polynomialNumerical method for solving a class of two-dimensional fractional optimal control problem of via operational matrices of Legendre polynomial1181527710.22055/jamm.2020.24146.1516FAYaserNouralizadeDepartment of Mathematics, Babol Noshirvani university of tecgnology, Babol, IranMahmoudBehroozifarDepartment of Mathematics, Babol Noshirvani university of tecgnology, Babol, IranMohsenAlipourDepartment of Mathematics, Babol Noshirvani university of tecgnology, Babol, IranJournal Article20171119 In this article, we present a numerical method for solving a class of two-dimensional fractional optimal control problems by the Legendre polynomial basis with fractional operational matrix. It should be mentioned that the dynamic system of the problem is based on the Caputo fractional partial derivative. This method, the dual integral is approximated by Gauss-Legendre rule, and then by using the Lagrangian equation, a nonlinear equation is obtained. This nonlinear equation set is solved by Newton's iterative method and unknown coefficients is determined. Finally, the proposed method was applied on a fractional problem with the different degree of fractional derivative. Also, the CPU time of method is exhibited. It is notable that all calculations were obtained by the Mathematica software. In this article, we present a numerical method for solving a class of two-dimensional fractional optimal control problems by the Legendre polynomial basis with fractional operational matrix. It should be mentioned that the dynamic system of the problem is based on the Caputo fractional partial derivative. This method, the dual integral is approximated by Gauss-Legendre rule, and then by using the Lagrangian equation, a nonlinear equation is obtained. This nonlinear equation set is solved by Newton's iterative method and unknown coefficients is determined. Finally, the proposed method was applied on a fractional problem with the different degree of fractional derivative. Also, the CPU time of method is exhibited. It is notable that all calculations were obtained by the Mathematica software.https://jamm.scu.ac.ir/article_15277_d4f8d53583a73342f0fdd4301316789f.pdf