  The general formalism of the free Dirac fermions on spatially flat
$(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetimes is
developed in momentum representation. The mode expansions in terms of the
fundamental spinors satisfying the charge conjugation and normalization
conditions are used for deriving the structure of the anti-commutator
matrix-functions and, implicitly, of the retarded, advanced, and Feynman
fermion propagators. The principal result is that the new type of integral
representation we proposed recently in the de Sitter case can be applied to the
Dirac fermions in any spatially flat FLRW geometry. Moreover, the Dirac
equation of the left-handed massless fermions can be analytically solved
finding a general spinor solution and deriving the integral representations of
the neutrino propagators. It is shown that in the Minkowski flat spacetime our
new integral representation is up to a change of variable just like the usual
Fourier representation of the fermion propagators. The form of the Feynman
propagator of the massive fermions on a spatially flat FLRW spacetime with a
scale factor of Milne-type is also outlined.
