Approximate controllability results for Sobolev-type delay differential system of fractional order without uniqueness

The main aim of this article is to focus on approximate controllability for Sobolev-type fractional control problems in Hilbert spaces without uniqueness. By using the fixed point theorem for multivalued maps with nonconvex values, the main results of our article are proved. Moreover, we obtain some results on the continuity of the solution map and the topological structure of the solution set of the considered Sobolev-type fractional differential system. Finally, we provide a theoretical application to assist in the effectiveness of our discussion.

Automated summary

The main aim of this article is to focus on the approximate controllability of Sobolev-type fractional control problems in Hilbert spaces without uniqueness. The main results of our article are proved by using the fixed point theorem for multivalued maps with nonconvex values. Moreover, we obtain some results on the continuity of the solution map and the topological structure of the solution set of the considered Sobolev-type fractional differential system.