  Hydrodynamics with both vector and axial currents is under study within a
holographic model, consisting of canonical $U(1)_V\times U(1)_A$ gauge fields
in an asymptotically AdS$_5$ black brane. When gravitational back-reaction is
taken into account, the chiral electric separation effect (CESE), namely the
generation of an axial current as the response to an external electric field,
is realized naturally. Via fluid/gravity correspondence, all the first order
transport coefficients in the hydrodynamic constitutive relations are evaluated
analytically: they are functions of vector chemical potential $\mu$, axial
chemical potential $\mu_5$ and the fluid's temperature $T$. Apart from the
proportionality factor $\mu\mu_5$, the CESE conductivity is found to be
dependent on the dimensionless quantities $\mu/T$ and $\mu_5/T$ nontrivially.
As a complementary study, frequency-dependent transport phenomena are revealed
through linear response analysis, demonstrating perfect agreement with the
results obtained from fluid/gravity correspondence.
