On semilinear fractional order differential inclusions in Banach spaces

We are considering the Cauchy problem for a semilinear fractional differential inclusion in a Banach space. By using the fixed point theory for condensing multivalued maps, we prove the local and global theorems of the existence of mild solutions to this problem. We verify the compactness of the solutions set and its continuous dependence on parameters and initial data. We demonstrate also the application of the averaging principle to the investigation of the continuous dependence of the solutions set on a parameter in the case when the right-hand side of the inclusion is rapidly oscillating. © 2017, House of the Book of Science. All rights reserved.

Авторы
Kamenskii M. 1 , Obukhovskii V. 2 , Petrosyan G.3 , Yao J.-C.4
Редакторы
-
Журнал
Издательство
House of the Book of Science
Номер выпуска
1
Язык
Английский
Страницы
269-292
Статус
Опубликовано
Подразделение
-
Номер
-
Том
18
Год
2017
Организации
  • 1 Faculty of Mathematics, Voronezh State University, RUDN University, 6 Miklukho-Malaya st, Moscow, 117198, Russian Federation
  • 2 Faculty of Physics and Mathematics, Voronezh State Pedagogical University, RUDN University, 6 Miklukho-Malaya st, Moscow, 117198, Russian Federation
  • 3 Faculty of Physics and Mathematics, Voronezh State Pedagogical University, Russian Federation
  • 4 Center for General Education, Kaohsiung Medical University, Taiwan
Ключевые слова
Averaging principle; Cauchy problem; Condensing map; Continuous dependence of solutions; Fixed point; Fractional differential inclusion; Measure of noncompactness; Multivalued map; Semilinear differential inclusion
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6045/