MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES
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 lea...
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2022-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/456 |
| _version_ | 1818163169661550592 |
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| author | Alena I. Machtakova Nikolai N. Petrov |
| author_facet | Alena I. Machtakova Nikolai N. Petrov |
| author_sort | Alena I. Machtakova |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T16:45:17Z |
| format | Article |
| id | doaj.art-99bba9aff373441785121bfe0944e936 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-12-11T16:45:17Z |
| publishDate | 2022-07-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-99bba9aff373441785121bfe0944e9362022-12-22T00:58:14ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522022-07-018110.15826/umj.2022.1.008143MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVESAlena I. Machtakova0Nikolai N. Petrov1Udmurt State University, 1 Universitetskaya Str., Izhevsk, 426034, Russia; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108Udmurt State University, 1 Universitetskaya Str., Izhevsk, 426034, Russia; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108In 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.https://umjuran.ru/index.php/umj/article/view/456differential game, group pursuit, pursuer, evader, fractional derivatives |
| spellingShingle | Alena I. Machtakova Nikolai N. Petrov MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES Ural Mathematical Journal differential game, group pursuit, pursuer, evader, fractional derivatives |
| title | MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES |
| title_full | MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES |
| title_fullStr | MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES |
| title_full_unstemmed | MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES |
| title_short | MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES |
| title_sort | matrix resolving functions in the linear group pursuit problem with fractional derivatives |
| topic | differential game, group pursuit, pursuer, evader, fractional derivatives |
| url | https://umjuran.ru/index.php/umj/article/view/456 |
| work_keys_str_mv | AT alenaimachtakova matrixresolvingfunctionsinthelineargrouppursuitproblemwithfractionalderivatives AT nikolainpetrov matrixresolvingfunctionsinthelineargrouppursuitproblemwithfractionalderivatives |