Abstract
In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.