  Fuzzy dark matter (FDM) is an attractive dark matter candidate motivated by
small scale problems in astrophysics and with a rich phenomenology on those
scales. We scrutinize the FDM model, more specifically the mass of the FDM
particle, through a dynamical analysis for the Galactic ultra-faint dwarf (UFD)
galaxies. We use a sample of 18 UFDs to place the strongest constraints to date
on the mass of the FDM particle, updating on previous bounds using a subset of
the sample used here. We find that most of the sample UFDs prefer a FDM
particle mass heavier than $10^{-21}\mathrm{eV}$. In particular, Segue 1
provides the strongest constraint, with
$m_\psi=1.1^{+8.3}_{-0.7}\times10^{-19}\mathrm{eV}$. The constraints found here
are the first that are compatible with various other independent cosmological
and astrophysical bounds found in the literature, in particular with the latest
bounds using the Lyman-$\alpha$ forest. We also find that the constraints
obtained in this work are not compatible with the bounds from luminous dwarf
galaxies, as already pointed out in the previous work using UFDs. This could
indicate that although a viable dark matter model, it might be challenging for
the FDM model to solve the small scale problems.
