Open AccessAntiperiodic Boundary Value Problem for a Semilinear Differential Equation of Fractional Order
Author(s) -
Garik Petrosyan
Publication year - 2020
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2020.34.51
Subject(s) - mathematics , boundary value problem , fixed point theorem , fractional calculus , mathematical analysis , banach space , separable space , fixed point , operator (biology) , order (exchange) , initial value problem , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
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.