## Mikhail Kamenskii, Garik Petrosyan, Ching-Feng Wen, An existence result for a periodic boundary value problem of fractional semilinear differential equations in a Banach space

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DOI: 10.23952/jnva.5.2021.1.10
Volume 5, Issue 1, 1 February 2021, Pages 155-177

Abstract. We consider the periodic boundary value problem for a semilinear differential equation of a fractional order $q\in (1,2)$ in a Banach space. We prove auxiliary statements about fractional derivatives. To solve this problem, we introduce the integral operator whose fixed points coincide with mild solutions of our problem. An existence result is established.