  Potential small-scale discrepancies in the picture of galaxy formation
painted by the $\Lambda$CDM paradigm have led to considerations of modified
dark matter models. One such dark matter model that has recently attracted much
attention is fuzzy dark matter (FDM). In FDM models, the dark matter is
envisaged to be an ultra-light scalar field with a particle mass $m_{\rm FDM}
\sim 10^{-22} $ eV. This yields astronomically large de Broglie wavelengths
which can suppress small-scale structure formation and give rise to the
observed kpc-sized density cores in dwarf galaxies. We investigate the
evolution of the 21-cm signal during Cosmic Dawn and the Epoch of Reionization
(EoR) in $\Lambda$FDM cosmologies using analytical models. The delay in source
formation and the absence of small halos in $\Lambda$FDM significantly postpone
the Ly$\alpha$ coupling, heating, as well as the reionization of the neutral
hydrogen of the intergalactic medium. As a result, the absorption feature in
the evolution of the global 21-cm signal has a significantly smaller full width
at half maximum ($\Delta z \lesssim 3$), than $\Lambda$CDM ($\Delta z \simeq
6$). This alone rules out $m_{\rm FDM} < 6 \times 10^{-22}$ eV as a result of
the $2\sigma$ lower limit $\Delta z \gtrsim 4$ from EDGES High-Band. As a
result, $\Lambda$FDM is not a viable solution to the potential small-scale
problems facing $\Lambda$CDM. Finally, we show that any detection of the 21-cm
signal at redshifts $z > 14$ by interferometers such as the SKA can also
exclude $\Lambda$FDM models.
