Abstract.

In this paper the Cauchy problem for fractional-order linear differential equations with constant coefficients is considered. Firstly, the given equation is reduced to the normal system, where only two elements of the initial condition vector are known. Then the quadratic functional is introduced for defining the optimal program trajectory and optimal control. The extended functional is constructed and some transformations in this functional have been done for obtaining the Euler-Lagrange equations with boundary conditions. Using the Mittag-Leffler function, we construct the fundamental solution matrix for the general case. Using this solution, initial condition and boundary condition with Lagrange multipliers we find the optimal program trajectory and optimal control.

Keywords:

quadratic functional, Euler-Lagrange equations, fractional-order derivative, Mittag Leffler function.