  In the fuzzy dark matter (FDM) model, dark matter is composed of ultra-light
particles with a de Broglie wavelength of $\sim$kpc, above which it behaves
like cold dark matter (CDM). Due to this, FDM suppresses the growth of
structure on small scales, which delays the onset of the cosmic dawn (CD) and
the subsequent epoch of reionization (EoR). This leaves potential signatures in
the sky averaged 21-cm signal (global), as well as in the 21-cm fluctuations,
which can be sought for with ongoing and future 21-cm global and intensity
mapping experiments. To do so reliably, it is crucial to include effects such
as the dark-matter/baryon relative velocity and Lyman-Werner star-formation
feedback, which also act as delaying mechanisms, as well as CMB and \lya
heating effects, which can significantly change the amplitude and timing of the
signal, depending on the strength of X-ray heating sourced by the remnants of
the first stars. Here we model the 21-cm signal in FDM cosmologies across CD
and EoR using a modified version of the public code 21cmvFAST that accounts for
all these additional effects, and is directly interfaced with the Boltzmann
code CLASS so that degeneracies between cosmological and astrophysical
parameters can be fully explored. We examine the prospects to distinguish
between the CDM and FDM models and forecast joint astrophysical, cosmological
and FDM parameter constraints achievable with intensity mapping experiments
such as HERA and global signal experiments like EDGES. We find that HERA will
be able to detect FDM particle masses up to $m_{\rm FDM}\! \sim
\!10^{-19}\,{\rm eV}\!-\!10^{-18}\,{\rm eV}$, depending on foreground
assumptions, despite the mitigating effect of the delaying and heating
mechanisms included in the analysis.
