A numerical method for solving variable order fractional optimal control problems

Document Type : Research Paper


1 Department of Mathematics , Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran

2 Department of Mathematics, University of Mazandaran, Babolsar, Iran

3 Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa


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.