LAUSR

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 HilleYosida 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 (Theorem 3.2). Theorem 3.3 gives an example of a concrete realization of this result. Some important particular cases including a nonlocal Cauchy problem, periodic and anti-periodic boundary value problems are presented.