Abstract:
The existence of a unique strong solution for the Cauchy problem to semilinear nondegenerate fractional dierential equation and for the generalized Showalter - Sidorov problem to semilinear fractional dierential 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.
\Bibitem{Ple16}
\by Marina~V.~Plekhanova
\paper Degenerate distributed control systems with fractional time derivative
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 2
\pages 58--71
\mathnet{http://mi.mathnet.ru/umj21}
\crossref{https://doi.org/10.15826/umj.2016.2.006}
\zmath{https://zbmath.org/?q=an:1424.49007}
\elib{https://elibrary.ru/item.asp?id=27447886}
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This publication is cited in the following 7 articles:
M. V. Plekhanova, A. F. Shuklina, “Smeshannoe upravlenie dlya polulineinykh uravnenii drobnogo poryadka”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 212, VINITI RAN, M., 2022, 64–72
M. V. Plekhanova, A. F. Shuklina, “Smeshannoe upravlenie dlya lineinykh beskonechnomernykh sistem drobnogo poryadka”, Chelyab. fiz.-matem. zhurn., 5:1 (2020), 32–43
G. D. Baibulatova, “Zadacha startovogo upravleniya dlya odnogo klassa vyrozhdennykh uravnenii s mladshimi drobnymi proizvodnymi”, Chelyab. fiz.-matem. zhurn., 5:3 (2020), 271–284
Marina V. Plekhanova, Guzel D. Baybulatova, Trends in Mathematics, Transmutation Operators and Applications, 2020, 573
Marina Plekhanova, Guzel Baybulatova, “Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems”, Mathematics, 8:4 (2020), 483
Marina V. Plekhanova, Guzel D. Baybulatova, Lecture Notes in Computer Science, 11548, Mathematical Optimization Theory and Operations Research, 2019, 501
L. N. Plekhanova, “Anthropogenic Degradation of Soils on River Terraces in the Volga–Ural Region in the Bronze Age and Its Effect on the Modern Soil–Plant Cover”, Arid Ecosyst, 9:3 (2019), 187
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