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This article is cited in 1 scientific paper (total in 1 paper)
Matrix resolving functions in the linear group pursuit problem with fractional derivatives
Alena I. Machtakovaab, Nikolai N. Petrovab a Udmurt State University, Izhevsk
b N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Abstract:
In finite-dimensional Euclidean space, we analyze the problem of pursuit of a single evader by a group of pursuers, which is described by a system of differential equations with Caputo fractional derivatives of order $\alpha$. The goal of the group of pursuers is the capture of the evader by at least m different pursuers (the instants of capture may or may not coincide). As a mathematical basis, we use matrix resolving functions that are generalizations of scalar resolving functions. We obtain sufficient conditions for multiple capture of a single evader in the class of quasi-strategies. We give examples illustrating the results obtained.
Keywords:
differential game, group pursuit, pursuer, evader, fractional derivatives.
Citation:
Alena I. Machtakova, Nikolai N. Petrov, “Matrix resolving functions in the linear group pursuit problem with fractional derivatives”, Ural Math. J., 8:1 (2022), 76–89
Linking options:
https://www.mathnet.ru/eng/umj163 https://www.mathnet.ru/eng/umj/v8/i1/p76
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Abstract page: | 120 | Full-text PDF : | 48 | References: | 28 |
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