The present paper is concerned with an antiperiodic boundary value problem for a semilinear differential equation with Caputo fractional derivative of order q ∈ (1, 2) considered in a separable Banach space. To prove the existence of a solution to our problem, we construct the Green’s function corresponding to the problem employing the theory of fractional analysis and properties of the Mittag-Leffler function . Then, we reduce the original problem to the problem on existence of fixed points of a resolving integral operator. To prove the existence of fixed points of this operator we investigate its properties based on topological degree theory for condensing mappings and use a generalized B.N. Sadovskii-type fixed point theorem.

Garik Petrosyan, Cand. Sci. (Phys.–Math.), Leading Researcher, Research Center, Voronezh State University of Engineering Technologies, 19, Revolutsii Prospect, Voronezh, 394036, Russian Federation, tel.: (3952)242210, e-mail: garikpetrosyan@yandex.ru

Petrosyan G.G. Antiperiodic Boundary Value Problem for a Semilinear Differential Equation of Fractional Order. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 34, pp. 51-66. https://doi.org/10.26516/1997-7670.2020.34.51

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