  For a many-to-one matching market where firms have strict and
$\boldsymbol{q}$-responsive preferences, we give a characterization of the set
of strongly stable fractional matchings as the union of the convex hull of all
connected sets of stable matchings. Also, we prove that a strongly stable
fractional matching is represented as a convex combination of stable matchings
that are ordered in the common preferences of all firms.
