RT Journal Article ID 2cdade146bdd37c2 A1 Chikriy, Arkadiy A. A1 Chentsov, Alexander G. A1 Matychyn, Ivan I. T1 Differential Games of the Fractional Order with Separated Dynamics JF Journal of Automation and Information Sciences JO JAI(S) YR 2009 FD 2009-12-30 VO 41 IS 11 SP 17 OP 27 K1 differential game K1 fractional derivative K1 separated dynamics K1 the method of resolving functions K1 approach problem in a guaranteed time AB Game approach problems for linear conflict controlled processes with fractional derivatives of arbitrary order are studied. The classical fractional Riemann-Liouville derivatives, regularized Dzhrbashyan-Nersesyan or Caputo derivatives as well as sequential Miller-Ross derivatives are considered. For the fixed controls of players, the solutions in the form of analogs of the Cauchy formula, with the use of the generalized matrix functions of Mittag-Leffler, are determined. The method of resolving functions is used as the basic one, which allows to obtain the sufficient conditions for the solvability of the approach problem in a guaranteed time. The results are illustrated by the model example of a game problem with separated motions of the fractional order π and e. PB Begell House LK https://www.dl.begellhouse.com/journals/2b6239406278e43e,0f8bdb634d301c54,2cdade146bdd37c2.html