ON CONTROLLABILITY FOR A SYSTEM GOVERNED BY A SEMILINEAR FRACTIONAL FUNCTIONAL DIFFERENTIAL INCLUSION WITH A NONCONVEX-VALUED RIGHT-HAND SIDE IN A BANACH SPACE

In this paper we study the controllability for a system governed by a fractional semilinear functional differential inclusion with an almost lower semicontinuous nonconvex-valued nonlinearity and a closed linear operator generating a C0–semigroup in a separable Banach space. We define the multivalued operator in the space of continuous functions whose fixed points are generating solutions of the problem. By using the fixed point theory for condensing multivalued maps and the methods of fractional analysis we study the properties of this mltioperator, in particular, we demonstrate that under certain conditions it is condensing w.r.t. an appropriate measure of noncompactness. This allows to present the controllability principle as the main result of the paper.