Geodesic
Matrix resolving functions in the linear group pursuit problem with fractional derivatives
Ural mathematical journal, Tome 8 (2022) no. 1, pp. 76-89

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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. 
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     author = {Alena I. Machtakova and Nikolai N. Petrov},
     title = {Matrix resolving functions in the linear group pursuit problem with fractional derivatives},
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Alena I. Machtakova; Nikolai N. Petrov. Matrix resolving functions in the linear group pursuit problem with fractional derivatives. Ural mathematical journal, Tome 8 (2022) no. 1, pp. 76-89. http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a7/