- PII
- 10.31857/S0374064124110067-1
- DOI
- 10.31857/S0374064124110067
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 60 / Issue number 11
- Pages
- 1499-1518
- Abstract
- For feedback systems governed by fractional semilinear differential inclusions and a sweeping process in a Hilbert space, controllability conditions are found. For the proof, topological methods of nonlinear analysis for multivalued condensing maps are used.
- Keywords
- задача управляемости дифференциальное включение sweeping процесс дробная производная уплотняющее отображение мера некомпактности
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 8
References
- 1. Balachandran, K. Controllability of nonlinear systems in Banach spaces: a survey / K. Balachandran, J.P. Dauer //J. Optim. Theory Appl. — 2002. — V. 115. — P. 7-28.
- 2. Benedetti, I. Controllability for impulsive semilinear functional differential inclusions with a noncompact evolution operator / I. Benedetti, V. Obukhovskii, P. Zecca // Discuss. Math. Differ. Incl. Control Optim. — 2011. — V. 31. — P. 39-69.
- 3. Gorniewicz, L. Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces / L. Gorniewicz, S.K. Ntouyas, D. O’Regan // Rep. Math. Phys. — 2005. — V. 56. — P. 437-470.
- 4. Monteiro Marques, M.D.P. Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction / M.D.P. Monteiro Marques // Progress Nonlin. Differ. Equat. Appl. — 1993. — V. 9.
- 5. Valadier, M. Rafle et viabilite / M. Valadier // Sem. Anal. Convexe Exp. — 1992. — V. 22, № 17.
- 6. Edmond, J.F. Relaxation of an optimal control problem involving a perturbed sweeping process / J.F. Edmond, L. Thibault // Math. Program. Ser. B. — 2005. — V. 104. — P. 347-373.
- 7. Толстоногов, А.А. Локальные условия существования решений процессов выметания / А.А. Тол-стоногов // Мат. сб. — 2019. — Т. 210, № 9. — С. 107-128.
- 8. Kilbas, A.A. Theory and Applications of Fractional Differential Equations / A.A. Kilbas, H.M. Sriva-stava, J.J. Trujillo. — Amsterdam : Elsevier Science B.V., North-Holland Mathematics Studies, 2006.
- 9. Podlubny, I. Fractional Differential Equations / I. Podlubny. — San Diego : Academic Press, 1999.
- 10. Gomoyunov, M.I. Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems / M.I. Gomoyunov // Fract. Calc. Appl. Anal. — 2018. — V. 21. — P. 1238-1261.
- 11. On semilinear fractional differential inclusions with a nonconvex-valued right-hand side in Banach spaces / V. Obukhovskii, G. Petrosyan, C.F. Wen, V. Bocharov // J. Nonlin. Var. Anal. — 2022. — V. 6, № 3. — P. 185-197.
- 12. Петросян, Г.Г. О краевой задаче для класса дифференциальных уравнений дробного порядка типа Ланжевена в банаховом пространстве / Г.Г. Петросян // Вестн. Удмурт. ун-та. Математика. Механика. Компьют. науки. — 2022. — Т. 32, № 3. — С. 415-432.
- 13. Zhou, Y. Existence of mild solutions for fractional neutral evolution equations / Y. Zhou, F. Jiao // Comput. Math. Appl. — 2010. — V. 59. — P. 1063-1077.
- 14. Kamenskii, M. Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces / M. Kamenskii, V. Obukhovskii, P. Zecca. — Berlin ; New-York : Walter de Gruyter, 2001.
- 15. Введение в теорию многозначных отображений и дифференциальных включений / Ю.Г. Борисович, Б.Д. Гельман, А.Д. Мышкис, В.В. Обуховский. — М. : Книжный дом “Либроком”, 2011. — 224 с.
- 16. Mainardi, F. On the initial value problem for the fractional diffusion-wave equation / F. Mainardi, S. Rionero, T. Ruggeri // Waves and Stability in Continuous Media. — 1994. — P. 246-251.
- 17. Nigmatullin, R.R. The realization of the generalized transfer equation in a medium with fractal geometry / R.R. Nigmatullin // Phys. Status Solidi B. — 1986. — V. 133. — P. 425-430.
