ON A TOPOLOGICAL STRUCTURE OF A SOLUTION SET TO A CAUCHY PROBLEM FOR FRACTIONAL DIFFERENTIAL INCLUSIONS WITH A UPPER SEMICONTINUOUS RIGHT-HAND SIDE

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Рұқсат ақылы немесе тек жазылушылар үшін

Аннотация

In this paper, we study the topological structure of a solution set to the Cauchy problem for semilinear differential inclusions of fractional order α ∈ (1, 2) in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by a upper semicontinuous multivalued operator of Caratheodory type. It is established that the set of solutions to the problem is an Rδ-set.

Авторлар туралы

G. Petrosyan

Voronezh State Pedagogical University

Email: garikpetrosyan@yandex.ru
Voronezh, Russia

Әдебиет тізімі

  1. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations. Amsterdam: Elsevier Science B.V., North-Holland Mathematics Studies, 2006.
  2. Podlubny I. Fractional differential equations. San Diego: Academic Press, 1999.
  3. Обуховский В.В., Петросян Г.Г., Сорока М.С. О начальной задаче для невыпуклозначных дифференциальных включений дробного порядка в банаховом пространстве // Математические заметки. 2024. Т. 115. № 3. 392–407.
  4. Петросян Г.Г. О краевой задаче для класса дифференциальных уравнений дробного порядка типа Ланжевена в банаховом пространстве // Вестник Удмуртского университета. Математика. Механика. Компьютерные науки. 2022. Т. 32. № 3. 415–432.
  5. Benedetti I., Obukhovskii V., Taddei V. On generalized boundary value problems for a class of fractional differential inclusions // Fract. Calc. Appl. Anal. 2017. V. 20. 1424–1446.
  6. Гомоюнов М.И. К теории дифференциальных включений с дробными производными Капуто // Дифференциальные уравнения. 2020. Т. 56. № 11. 1419–1432.
  7. Ke T.D., Obukhovskii V., Wong N.C., Yao J.C. On a class of fractional order differential inclusions with infinite delays // Applicable Anal. 2013. V. 92. 115–137.
  8. Kamenskii M.I., Obukhoskii V.V., Petrosyan G.G., Yao J.C. Boundary value problems for semilinear differential inclusions of fractional order in a Banach space // Applicable Analysis. 2017. V. 97. № 4. 571–591.
  9. Aronszajn N. Le correspondant topologique de l’unicite dans la theorie des equations differentielles // Annals of mathematics, second series. 1942. V. 43. № 4. 730–738. [in French]
  10. Go´rniewicz L. On the solution sets of differential inclusions // J. Math. Anal. and Appl. 1986. V. 113. № 1. 235–244.
  11. Филиппов В.В. О теореме Ароншайна // Дифференциальные уравнения. 1997. Т. 33. № 1. 75–79.
  12. Go´rniewicz L. Topological Fixed Point Theory of Multivalued Mappings, Second edition. Topological Fixed Point Theory and Its Applications. Dordrecht: Springer, 2006.
  13. Djebali S., Go´rniewicz L., Ouahab A. Solution Sets for Differential Equations and Inclusions. De Gruyter Series in Nonlinear Analysis and Applications, 18. Berlin: Walter de Gruyter, 2013.
  14. Kamenskii M., Obukhovskii V., Zecca P. Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. Berlin–New-York: Walter de Gruyter, 2001.
  15. Kamenskii M.I., Obukhoskii V.V., Petrosyan G.G. A continuous dependence of a solution set for fractional differential inclusions of an order q ∈ (1, 2) on parameters and initial data // Lobachevskii Journal of Mathematics. 2023. V. 44. № 8. 3331–3342.
  16. Sova M. Cosine operator functions. Rozprawy Mat. 49, 1966.
  17. Борисович Ю.Г., Гельман Б.Д., Мышкис А.Д., Обуховский В.В. Введение в теорию многоначных отображений и дифференциальных включений. М.: Книжный дом „Либроком“, 2011.
  18. Hyman D.H. On decreasing sequences of compact absolute retracts // Fund. Math. 1969. V. 64. 91–97.
  19. Zhou Y., Jiao F. Existence of mild solutions for fractional neutral evolution equations // Comput. Math. Appl. 2010. V. 59. 1063–1077.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML

© Russian Academy of Sciences, 2025