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Abstract <p> In a finite-dimensional Euclidean space, we consider the problem of pursuing a group ofevaders by a group of pursuers described by a linear nonstationary system of differential equationswith fractional Caputo derivatives. The sets of admissible players’ controls—compact sets,terminal sets—the origin of coordinates. Sufficient conditions have been obtained for thecapture of at least one evader and all evaders under the condition that the evaders use the samecontrol. In the study, the method of matrix and scalar resolving functions is used as a basic one. Itis shown that differential games described by equations with fractional derivatives have propertiesthat are different from those of differential games described by ordinary differential equations.</p>

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On the Problem of Pursuing a Group of Coordinated Evaders in a Game with Fractional Derivatives

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • N. N. Petrov,
  • A. I. Machtakova

摘要

Abstract

In a finite-dimensional Euclidean space, we consider the problem of pursuing a group ofevaders by a group of pursuers described by a linear nonstationary system of differential equationswith fractional Caputo derivatives. The sets of admissible players’ controls—compact sets,terminal sets—the origin of coordinates. Sufficient conditions have been obtained for thecapture of at least one evader and all evaders under the condition that the evaders use the samecontrol. In the study, the method of matrix and scalar resolving functions is used as a basic one. Itis shown that differential games described by equations with fractional derivatives have propertiesthat are different from those of differential games described by ordinary differential equations.