Mikhail Kamenskii, Valeri Obukhovskii, Garik Petrosyan, Maria Soroka, On topological properties of solution sets for semilinear differential inclusions of fractional order $\alpha\in (1,2)$ with non-convex right-hand sides, Vol. 2026 (2026), No. 26, pp. 1-15

Full Text: PDF
DOI: 10.23952/cot.2026.26

Received January 27, 2025; Accepted April 11, 2025; Published online March 2, 2026

Abstract. In this paper, we study the Cauchy problem for a semilinear differential inclusion of a fractional order $\alpha\in (1,2)$ with a nonconvex-valued almost lower semicontinuous nonlinearity and a linear closed operator generating a family of cosine operator functions. By using the theory of measure of noncompactness and condensing operators theory we study topological properties of the solution set of this problem. We prove that the solution set of the Cauchy problem possesses the classical Kneser connectedness property.

How to Cite this Article:
M. Kamenskii, V. Obukhovskii, G. Petrosyan, M. Soroka, On topological properties of solution sets for semilinear differential inclusions of fractional order $\alpha\in (1,2)$ with non-convex right-hand sides, Commun. Optim. Theory 2026 (2026) 26.