BPs Operational Matrices for Solving Time Varying Fractional Optimal Control Problems

In this paper, we present a method for solving time varying fractional optimal control problems by Bernstein polynomials. Firstly, we derive the Bernstein polynomials (BPs) operational matrix for the fractional derivative in the Caputo sense, which has not been undertaken before. This method reduces the problems to a system of algebraic equations. The results obtained are in good agreement with the existing ones in open literatures and the solutions approach to classical solutions as the order of the fractional derivatives approach to 1.