Progress in Fractional Differentiation & Applications

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We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order α ∈ (0, 1). Basing on the finite-difference Gr¨unwald-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.

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