  We show that the response, frozen and semifreddo fractional susceptibility
functions of certain real-analytic unimodal families, at Misiurewicz parameters
and for fractional differentiation index $0\le\eta<1/2$, are holomorphic on a
disk of radius greater than one. This is a step towards solving a conjecture of
Baladi and Smania, in the case of the aforementioned susceptibility functions.
