DOI: 10.24193/fpt-ro.2021.1.20

Authors: Valeri Obukhovskii, Pietro Zecca and Maria Afanasova

Abstract: We consider a nonlocal boundary value problem for a semilinear differential inclusion of a fractional order in a Banach space assuming that its linear part is a non-densely defined Hille-Yosida operator. We apply the theory of integrated semigroups, fractional calculus and the fixed point theory of condensing multivalued maps to obtain a general existence principle. An example of a concrete realization of this result is also given. Some important particular cases including a nonlocal Cauchy problem, periodic and anti-periodic boundary value problems are presented.

Key Words and Phrases: Fractional differential inclusion, boundary value problem, nonlocal Cauchy problem, periodic problem, Hille-Yosida operator, integrated semigroup, measure of noncompactness, fixed point, topological degree, multivalued map, condensing map.

2010 Mathematics Subject Classification: 34B10, 34A08, 34A60, 34C25, 34G25, 47D62, 47H04, 47H08, 47H10, 47H11.

Published on-line: February 1st, 2021.

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