ON THE EXISTENCE OF A SOLUTION OF A PERIODIC BOUNDARY VALUE PROBLEM FOR SEMILINEAR DIFFERENTIAL INCLUSIONS OF FRACTIONAL ORDER FROM THE INTERVAL (3,4) IN BANACH SPACES
DOI:
https://doi.org/10.52575/2687-0959-2021-53-4-266-283Keywords:
differential inclusion, fractional derivative, Green's function, condensing multioperator, measure of noncompactness, fixed point.Abstract
In this paper we study a periodic boundary value problem for a class of semilinear differential inclusions of fractional order from the interval (3,4) in a Banach space for which the multivalued nonlinearity satisfies the regularity condition expressed in terms of measures of noncompactness. We prove the existence of a solution to the problem, we first construct the corresponding Green's function. Then we introduce into consideration a multivalued resolving operator in the space of continuous functions and reduce the problem posed to the problem of the existence of fixed points of a resolving multioperator. We prove the existence of fixed points, by using a generalized B.N. Sadovskii type theorem.
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