Fractional delay control problems: topological structure of solution sets and its applications

Abstract

This paper deals with the control problems of semilinear fractional delay evolution equations. Under rather mild conditions, we study the topological structure of solution sets (compactness and Rδ-property). Then, the information about the structure is employed to show the invariance of a reachability set of the control problem under nonlinear perturbations. Finally, we present an example to illustrate the feasibility of the abstract results.