Numerical method for solving a class of two-dimensional fractional optimal control problem of via operational matrices of Legendre polynomial

Document Type : Original Paper


Department of Mathematics, Babol Noshirvani university of tecgnology, Babol, Iran


‎ ‎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.


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