  We study fermionic superfluidity in a boson-single-species-fermion cold atom
mixture. We argue that apart from the standard p-wave fermion pairing mediated
by the phonon field of the boson gas, the system also exhibits s-wave pairing
with the anomalous correlator being an odd function of time or frequency. We
show that such a superfluid phase can have a much higher transition temperature
than the p-wave and may exist for sufficiently strong couplings between
fermions and bosons. These conditions for odd-frequency pairing are favorable
close to the value of the coupling at which the mixture phase-separates. We
evaluate the critical temperatures for this system and discuss the experimental
realization of this superfluid in ultracold atomic gases.
