Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45367220210401Solution of the Problem of Analytical Construction of Optimal Regulators for a Fractional Order Oscillatory System in the General Case9709761646210.22055/jacm.2021.35130.2572ENFikret AAlievInstitute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan0000-0001-5402-8920Nihan AAlievInstitute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan0000-0001-8531-8648Nargiz A.SafarovaInstitute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan0000-0003-3829-8896Yegana VahidMamedovaInstitute of Applied Mathematics, Baku State University, Z. Khalilov, 23, AZ1148 Baku, Azerbaijan0000-0003-1307-7894Journal Article20200922An algorithm is proposed for solving the problem of analytical constructing of an optimal fractional-order regulator (OFOR) in the general case. By inscribing the extended functional, the corresponding fractional order Euler-Lagrange equation is determined. Then, using the Mittag-Leffler function, a fundamental solution to the corresponding Hamiltonian system is constructed. It is shown that to obtain an analogue of the analytical construction of AM Letov's regulators, the order of the fractional derivatives must be a rational number, the denominator and numerator of which are odd numbers. Numerical illustrative examples are provided.https://jacm.scu.ac.ir/article_16462_7b8d482401be8a8a0685cd87afcbbc01.pdf