  We consider a conflict-controlled dynamical system described by a nonlinear
ordinary fractional differential equation with the Caputo derivative of an
order $\alpha \in (0, 1).$ Basing on the finite-difference
Gr\"{u}nwald-Letnikov formulas, we propose an approximation of the considered
system by a system described by a functional-differential equation of a
retarded type. A mutual aiming procedure between the initial
conflict-controlled system and the approximating system is given that
guarantees the desired proximity between their motions. This procedure allows
to apply, via the approximating system, the results obtained for
functional-differential systems for solving control problems in fractional
order systems. Examples are considered, results of numerical simulations are
presented.
