ON SEMILINEAR FRACTIONAL ORDER DIFFERENTIAL INCLUSIONS IN BANACH SPACES

被引：22

作者：

Kamenskii, Mikhail ^{[1
,2
]}

Obukhovskii, Valeri ^{[3
,4
]}

Petrosyan, Garik ^{[3
]}

Yao, Jen-Chih ^{[5
]}

机构：

[1] Voronezh State Univ, Fac Math, 6 Miklukho Malaya st, Moscow 117198, Russia

[2] RUDN Univ, Fac Math, 6 Miklukho Malaya st, Moscow 117198, Russia

[3] Voronezh State Pedag Univ, Fac Math & Phys, 6 Miklukho Malaya st, Moscow 117198, Russia

[4] RUDN Univ, 6 Miklukho Malaya st, Moscow 117198, Russia

[5] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung, Taiwan

来源：

FIXED POINT THEORY | 2017年 / 18卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Fractional differential inclusion; semilinear differential inclusion; Cauchy problem; continuous dependence of solutions; averaging principle; fixed point; multivalued map; condensing map; measure of noncompactness; EXISTENCE;

D O I：

10.24193/fpt-ro.2017.1.22

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：269 / 291

页数：23

共 50 条

[1] Nonlocal Cauchy problems for semilinear differential inclusions with fractional order in Banach spaces
Wang, JinRong
Ibrahim, A. G.
Feckan, Michal
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 27 (1-3) : 281 - 293
[2] Existence results for fractional semilinear differential inclusions in Banach spaces
Liu X.
Liu Z.
[J]. Liu, X. (liuxiaoyou2002@hotmail.com), 2013, Springer Verlag (42) : 171 - 182
[3] Semilinear Differential Inclusions in Separable Banach Spaces
薛星美
宋国柱
[J]. Communications in Mathematical Research, 1995, (02) : 151 - 156
[4] ON BOUNDED SOLUTIONS OF SEMILINEAR FRACTIONAL ORDER DIFFERENTIAL INCLUSIONS IN HILBERT SPACES
Kamenskii, M.
Kornev, S.
Obukhovskii, V.
Wong, N. C.
[J]. JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2021, 5 (02): : 251 - 265
[5] Boundary value problems for semilinear differential inclusions of fractional order in a Banach space
Kamenskii, Mikhail
Obukhovskii, Valeri
Petrosyan, Garik
Yao, Jen-Chih
[J]. APPLICABLE ANALYSIS, 2018, 97 (04) : 571 - 591
[6] Differential Equations and Inclusions of Fractional Order with Impulse Effects in Banach Spaces
Ahmed Gamal Ibrahim
[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 69 - 109
[7] Differential Equations and Inclusions of Fractional Order with Impulse Effects in Banach Spaces
Ibrahim, Ahmed Gamal
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (01) : 69 - 109
[8] ON CONTROLLABILITY FOR FRACTIONAL DIFFERENTIAL INCLUSIONS IN BANACH SPACES
Wang, JinRong
Li, XueZhu
Wei, Wei
[J]. OPUSCULA MATHEMATICA, 2012, 32 (02) : 341 - 356
[9] Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces
Pavlackova, Martina
Taddei, Valentina
[J]. MATHEMATICS, 2022, 10 (04)
[10] Semilinear Conformable Fractional Differential Equations in Banach Spaces
Anjali Jaiswal
D. Bahuguna
[J]. Differential Equations and Dynamical Systems, 2019, 27 : 313 - 325

← 1 2 3 4 5 →