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In this paper an optimal control problem considered for linear dynamic systems of non-integer order.Investigation based on moment method application.Its shown that optimal control problem can be reduced to the classical problem of moments.For the last problem possibility of statement and solvability analyzed and corresponding conditions obtained.Some special cases considered for one-and two dimensional systems.In these cases an explicit solutions obtained for control with minimum norm at given time interval and for control with minimum transient time at given norm restriction.Behavior of control norm,transient time and phase trajectories studied.