Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 10 Special Issue ( Nonlinear Analysis in Engineering and Sciences) 2019 12 01 A Numerical Approach for Fractional Optimal Control Problems by Using Ritz Approximation 67 73 4397 10.22075/ijnaa.2019.4397 EN A. Ramezanpour Department of Mathematics, Payame Noor University, Tehran, Iran P. Reihani Department of Mathematics, Payame Noor University, Tehran, Iran J. Vahidi Department of Mathematics, Iran University of science and Technology, Tehran,Iran. Department of Mathematical Sciences, University of South Africa, UNISA0003,South Africa F. Soltanian Department of Mathematics, Payame Noor University, Tehran, Iran Journal Article 2019 05 02 In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the numerical solution is investigated. Some numerical examples are presented which illustrate the theoretical results and the performance of the method. https://ijnaa.semnan.ac.ir/article_4397_a856b9b607c47c03dbfdc2e0a8c1e883.pdf