DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE
The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved....
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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.
2016-11-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/48 |
| _version_ | 1818114853000183808 |
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| author | Marina V. Plekhanova |
| author_facet | Marina V. Plekhanova |
| author_sort | Marina V. Plekhanova |
| collection | DOAJ |
| description | The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal control problems to a system described by the degenerate semilinear fractional evolution equation. Abstract results are applied to the research of an optimal control problem solvability for the equations system of Kelvin–Voigt fractional viscoelastic fluids. |
| first_indexed | 2024-12-11T03:57:19Z |
| format | Article |
| id | doaj.art-02a09e7411ff408189872e1ae741a8a6 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-12-11T03:57:19Z |
| publishDate | 2016-11-01 |
| 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-02a09e7411ff408189872e1ae741a8a62022-12-22T01:21:45ZengKrasovskii 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 Journal2414-39522016-11-012210.15826/umj.2016.2.00622DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVEMarina V. Plekhanova0Computational Mechanics Department, South Ural State Universit and Laboratory of Quantum Topology, Chelyabinsk State University, ChelyabinskThe existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional differential equation and for the generalized Showalter–Sidorov problem to semilinear fractional differential equation with degenerate operator at the Caputo derivative in Banach spaces is proved. These results are used for search of solution existence conditions for a class of optimal control problems to a system described by the degenerate semilinear fractional evolution equation. Abstract results are applied to the research of an optimal control problem solvability for the equations system of Kelvin–Voigt fractional viscoelastic fluids.https://umjuran.ru/index.php/umj/article/view/48Fractional dierential calculus, Caputo deivative, Mittag-Leer function, Partial dierential equation, Degenerate evolution equation, Optimal control, Fractional viscoelastic fluid |
| spellingShingle | Marina V. Plekhanova DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE Ural Mathematical Journal Fractional dierential calculus, Caputo deivative, Mittag-Leer function, Partial dierential equation, Degenerate evolution equation, Optimal control, Fractional viscoelastic fluid |
| title | DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE |
| title_full | DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE |
| title_fullStr | DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE |
| title_full_unstemmed | DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE |
| title_short | DEGENERATE DISTRIBUTED CONTROL SYSTEMS WITH FRACTIONAL TIME DERIVATIVE |
| title_sort | degenerate distributed control systems with fractional time derivative |
| topic | Fractional dierential calculus, Caputo deivative, Mittag-Leer function, Partial dierential equation, Degenerate evolution equation, Optimal control, Fractional viscoelastic fluid |
| url | https://umjuran.ru/index.php/umj/article/view/48 |
| work_keys_str_mv | AT marinavplekhanova degeneratedistributedcontrolsystemswithfractionaltimederivative |