The authors are concerned with the existence of mild solutions for the fractional order semilinear functional differential inclusion of the form:
where is the standard Riemann-Liouville fractional derivative, is a multivalued function, is a separable real Banach space and is the family of all nonempty subsets of . The operator , densely defined possibly unbounded), is a generator of a strongly continuous semigroup of bounded linear operators from to . The function is a given continuous function such that . For any function defined on and any , denotes the element of defined by
Both cases of convex valued and nonconvex valued right hand side are considered. The proofs are, respectively, achieved by means of Martelli’s fixed point theorem and the contraction multivalued fixed point theorem due to Covitz and Nadler. The compactness of the set of mild solutions defined on is also proved.