  We study the mobility of Dirac fermions in monolayer graphene on a GaAs
substrate, restricted by the combined action of the extrinsic potential of
piezoelectric surface acoustical phonons of GaAs (PA) and of the intrinsic
deformation potential of acoustical eigen-phonons in graphene (DA). In the high
temperature ($T$) regime the momentum relaxation rate exhibits the same linear
dependence on $T$ but different dependences on the carrier density $n$,
corresponding to the mobility $\mu\propto 1/\sqrt{n}$ and $1/n$, respectively
for the PA and DA scattering mechanisms. In the low $T$ Bloch-Gr\"uneisen
regime, the mobility shows the same square-root density dependence, $\mu\propto
\sqrt{n}$, but different temperature dependences, $\mu\propto T^{-3}$ and $
T^{-4}$, respectively for PA and DA phonon scattering.
