## Valeri Obukhovskii, Garik Petrosyan, Ching-Feng Wen, Vladislav Bocharov, On semilinear fractional differential inclusions with a nonconvex-valued right-hand side in Banach spaces

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DOI: 10.23952/jnva.6.2022.3.02

Volume 6, Issue 3, 1 June 2022, Pages 185-197

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 fixed point theory for condensing maps, we prove the local and global theorems of the existence of a mild solution to this problem.