ON CONTROLLABILITY FOR A SYSTEM GOVERNED BY A FRACTIONAL-ORDER SEMILINEAR FUNCTIONAL DIFFERENTIAL INCLUSION IN A BANACH SPACE

We obtain some controllability results for a system governed by a semilinear functional differential inclusion of a fractional order in a Banach space assuming that the linear part of inclusion generates a noncompact Co-semigroup. We define the multivalued operator whose fixed points are generating solutions of the problem. By applying the methods of fractional analysis and the fixed point theory for condensing multivalued maps we study the properties of this operator, in particular, we prove that under certain conditions it is condensing w.r.t. an appropriate measure of noncompactness. This allows to present the general controllability principle in terms of the topological degree theory and to consider certain important particular cases.