Boundary value problems for semilinear differential inclusions of fractional order in a Banach space

被引：24

作者：

Kamenskii, Mikhail ^{[1
,2
]}

Obukhovskii, Valeri ^{[2
,3
]}

Petrosyan, Garik ^{[3
]}

Yao, Jen-Chih ^{[4
]}

机构：

[1] Voronezh State Univ, Fac Math, Voronezh, Russia

[2] RUDN Univ, Dept Nonlinear Anal & Optimizat, Moscow, Russia

[3] Voronezh State Pedag Univ, Fac Math & Phys, Voronezh, Russia

[4] China Med Univ, Ctr Gen Educ, Taichung, Taiwan

来源：

APPLICABLE ANALYSIS | 2018年 / 97卷 / 04期

关键词：

Differential inclusion; fractional derivative; solution set; R-delta-set; translation multioperator; measure of noncompactness; condensing multimap; fixed point; periodic problem; anti-periodic problem; EXISTENCE;

D O I：

10.1080/00036811.2016.1277583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we show that the solution set of a fractional order semilinear differential inclusion in a Banach space has the topological structure of an R-delta-set. This result allows to apply a fixed point result for condensing multimaps to the translation multioperator along the trajectories of such inclusion and to prove the existence of solutions satisfying periodic and anti-periodic boundary value conditions. An example concerning with a fractional order feedback control system is presented.

引用

页码：571 / 591

页数：21

共 50 条

[21] Boundary Value Problems for Fractional Differential Inclusions with Nonlocal Conditions
Hamani, Samira
Henderson, Johnny
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2016, 13 (03) : 967 - 979
[22] Some boundary value problems of fractional differential equations and inclusions
Ahmad, Bashir
Nieto, Juan J.
Pimentel, Johnatan
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1238 - 1250
[23] Boundary Value Problems for Fractional Differential Inclusions with Nonlocal Conditions
Samira Hamani
Johnny Henderson
[J]. Mediterranean Journal of Mathematics, 2016, 13 : 967 - 979
[24] On generalized boundary value problems for a class of fractional differential inclusions
Irene Benedetti
Valeri Obukhovskii
Valentina Taddei
[J]. Fractional Calculus and Applied Analysis, 2017, 20 : 1424 - 1446
[25] ON GENERALIZED BOUNDARY VALUE PROBLEMS FOR A CLASS OF FRACTIONAL DIFFERENTIAL INCLUSIONS
Benedetti, Irene
Obukhovskii, Valeri
Taddei, Valentina
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2017, 20 (06) : 1424 - 1446
[26] Boundary value problems for second order differential equations on unbounded domains in a Banach space
Liu, YS
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (2-3) : 569 - 583
[27] 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
[28] NEUMANN BOUNDARY-VALUE PROBLEMS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES
Aitalioubrahim, Myelkebir
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010,
[29] Antiperiodic Boundary Value Problem for a Semilinear Differential Equation of Fractional Order
Petrosyan, G. G.
[J]. BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS, 2020, 34 : 51 - 66
[30] Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space
Bragdi, Mabrouk
Debbouche, Amar
Baleanu, Dumitru
[J]. ADVANCES IN MATHEMATICAL PHYSICS, 2013, 2013

← 1 2 3 4 5 →