On the Aronszajn property for fractional neutral evolution equations with infinite delay on half-line

We establish an R_δ structure theorem for the fixed point set of the Krasnosel'skii type operator on Fréchet space. Applying this result, a topological structure for the set of all mild solutions of fractional neutral evolution equations with infinite delay on half-line is investigated. We show that the solution set is an R_δ-set.