Approximate controllability of fractional functional evolution inclusions with delay in Hilbert spaces

Recently, the problem of approximate controllability has been extensively studied by many authors. However, up to now approximate controllability problems for fractional functional evolution inclusions with delay have not been considered in the literature. To fill this gap, this paper investigate the approximate controllability problem for fractional functional evolution inclusions in Hilbert spaces. The results are obtained under the corresponding linear system is approximately controllable. By using the fixed-point theorem for condensing multivalued maps and semigroup theory, sufficient conditions are formulated and proved. In the end, we give two examples to illustrate the application of the abstract results.