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 32 条

[1]

Abbas S., 2012, TOPICS FRACTIONAL DI, DOI 10.1007/978-1-4614-4036-9

[2] NEW STABILITY RESULTS FOR PARTIAL FRACTIONAL DIFFERENTIAL INCLUSIONS WITH NOT INSTANTANEOUS IMPULSES [J].