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.
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