Geodesic
Antiperiodic boundary value problem for a semilinear differential equation of fractional order
The Bulletin of Irkutsk State University. Series Mathematics, Tome 34 (2020), pp. 51-66

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The present paper is concerned with an antiperiodic boundary value problem for a semilinear differential equation with Caputo fractional derivative of order $ q \in (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.
Keywords: Caputo fractional derivative, semilinear differential equation, boundary value problem, fixed point, condensing mapping, measure of noncompactness. 
@article{IIGUM_2020_34_a3,
     author = {G. G. Petrosyan},
     title = {Antiperiodic boundary value problem for a semilinear differential equation of fractional order},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {51--66},
     publisher = {mathdoc},
     volume = {34},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a3/}
}
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G. G. Petrosyan. Antiperiodic boundary value problem for a semilinear differential equation of fractional order. The Bulletin of Irkutsk State University. Series Mathematics, Tome 34 (2020), pp. 51-66. http://geodesic.mathdoc.fr/item/IIGUM_2020_34_a3/