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Journal of Automation and Information Sciences

年間 12 号発行

ISSN 印刷: 1064-2315

ISSN オンライン: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

Indexed in

Differential Games of the Fractional Order with Separated Dynamics

巻 41, 発行 11, 2009, pp. 17-27
DOI: 10.1615/JAutomatInfScien.v41.i11.20
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要約

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.

によって引用された
  1. Tarasov Vasily, On History of Mathematical Economics: Application of Fractional Calculus, Mathematics, 7, 6, 2019. Crossref

  2. Gomoyunov Mikhail I., Fractional Derivatives of Convex Lyapunov Functions and Control Problems in Fractional Order Systems, Fractional Calculus and Applied Analysis, 21, 5, 2018. Crossref

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