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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Druckformat: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v41.i11.20
pages 17-27

Differential Games of the Fractional Order with Separated Dynamics

Arkadiy A. Chikriy
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine
Alexander G. Chentsov
N.N. Krasovsky Institute of Mathematics and Mechanics of Ural Branch of Russian Academy of Sciences, Ural Federal University, Ekaterinburg
Ivan I. Matychyn
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine

ABSTRAKT

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.


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