Boundary value problems for semilinear differential inclusions of fractional order in a Banach space. Issue 4 (12th March 2018)

• Record Type: Journal Article
• Authors: Kamenskii, Mikhail; Obukhovskii, Valeri; Petrosyan, Garik; Yao, Jen-Chih
• Is Part Of: Applicable analysis. Volume 97:Issue 4(2018)
• Page Start: 571
• Page End: 591
• Publication Date: 2018-03-12
• Subjects: Differential inclusion -- fractional derivative -- solution set -- -set -- translation multioperator -- measure of noncompactness -- condensing multimap -- fixed point -- periodic problem -- anti-periodic problem; Primary: 34G25 -- 34A08 -- Secondary: 34A60 -- 34B15 -- 34C25 -- 47H04 -- 47H08 -- 47H10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1277583
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : 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 -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.