  We have derived the solutions of the relativistic anomalous
magnetohydrodynamics with longitudinal Bjorken boost invariance and transverse
electromagnetic fields in the presence of temperature or energy density
dependent electric conductivity. We consider the equations of states in a high
temperature limit or in a high chiral chemical potential limit. We obtain both
perturbative analytic solutions up to the order of \hbar and numerical
solutions in our configurations of initial electromagnetic fields and Bjorken
flow velocity. Our results show that the temperature or energy density
dependent electric conductivity plays an important role to the decaying of the
energy density and electromagnetic fields. We also implement our results to the
splitting of global polarization for \Lambda and \bar{\Lambda} hyperons induced
by the magnetic fields. Our results for the splitting of global polarization
disagree with the experimental data in low energy collisions, which implies
that the contribution from gradient of chemical potential may dominate in the
low energy collisions.
