  We study single lepton production from semileptonic decays of heavy flavor
hadrons ($D,B\rightarrow~l$) in pp and p$A$ collisions at RHIC and the LHC
within the saturation/Color-Glass-Condensate (CGC) framework. Using the gluon
distribution function obtained with the dipole amplitude, whose energy
dependence is described by the Balitsky-Kovchegov equation with running
coupling effect, we compute the transverse-momentum ($p_\perp$) spectra of the
lepton yields at mid and forward rapidities. We find that a large fraction of
leptons at low $p_\perp$ stems from the saturation regime of the incoming
gluons in the target, especially in p$A$ collisions at the LHC. The resultant
$p_\perp$ spectra is slightly harder than the data, but the nuclear
modification factor seems consistent with the data within some uncertainty. We
also update the nuclear modification factors for J/$\psi$ and $D$ meson at the
LHC energy.
