a numerical method for solving variable order fractional optimal control problems

This study is devoted to introducing a computational technique based on bernstein polynomials to solve variable order fractional optimal control problems (vo-focps). this class of problems generated by dynamical systems describe with variable order fractional derivatives in the caputo sense. in the proposed method, the bernstein operational matrix of the fractional variable-order derivatives will be derived. then, this matrix is used to obtain an approximate solution to mentioned problems. with the use of gauss-legendre quadrature rule and the mentioned operational matrix, the considered vo-focps are reduced to a system of equations that are solved to get approximate solutions. the obtained results show the accuracy of the numerical technique.