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.
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Acknowledgements
The work on the paper was carried out during Prof. V. Obukhovskii’s and Prof. M. Kamenskii’s visit to the Center for Fundamental Science, Kaohsiung Medical University and the Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan in 2016. They would like to express their gratitude to the members of the Center and the Department for their kind hospitality. The authors are grateful to anonymous referees for their valuable remarks. The work of the first, second and the third author is supported by the Ministry of Education and Science of the Russian Federation in the frameworks of the project part of the state work quota (Project No 1.3464.2017).
Notes
No potential conflict of interest was reported by the authors.