Valeri Obukhovskii, Garik Petrosyan, Maria Soroka, Jen-Chih Yao, On topological properties of solution sets of semilinear fractional differential inclusions with non-convex right-hand side

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DOI: 10.23952/jnva.8.2024.1.05

Volume 8, Issue 1, 1 February 2024, Pages 95-108

Abstract. In this paper, we study the Cauchy problem for a semilinear fractional order differential inclusion with a nonconvex-valued almost lower semicontinuous nonlinearity and a linear closed operator generating a $C_{0}$ -semigroup in a separable Banach space. By using the theory of measure of noncompactness and condensing operators, 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:
V. Obukhovskii, G. Petrosyan, M. Soroka, J.C. Yao, On topological properties of solution sets of semilinear fractional differential inclusions with non-convex right-hand side, J. Nonlinear Var. Anal. 8 (2024), 95-108.