Numerical study on multi-order multi-dimensional fractional optimal control problem in general form - Mohsen Alipour (Kuwait Journal of Science)
The aim of this work is application of Bernstein polynomials (BPs) for solving multi-order multidimensional fractional optimal control problem (MOMDFOCP). Firstly, by the Bernstein basis, we introduce operational matrices for Riemann-Liouville fractional integral and product. Then, via these matrices, we reduce the problem to the optimization problem. For solving this problem, we apply Lagrangian multipliers method. So, we can obtain approximate solution for MOMDFOCP. Results of some examples show that the obtained solutions are very accurate and in good agreement with exact solutions.