  With the inclusion of the isovector scalar channel in the meson-nucleon
couplings, taking DD-ME$\delta$ as an effective interaction, the moments of
inertia of neutron stars possessing various stellar masses are studied within
the density dependent relativistic mean field (RMF) theory. The isovector
scalar channel contributes to the softening of the neutron-star matter equation
of state (EOS) and therefore the reduction of the maximum mass and radius of
neutron stars. Smaller values of the total moment of inertia $I$ and the
crustal moment of inertia $\Delta{I}$ are then obtained in DD-ME$\delta$ via
numerical procedure in comparison with those in other selected RMF functionals.
In addition, the involvement of the isovector scalar channel lowers the
thickness of the neutron star crust and its mass fraction as well. The
sensitivity to both the crustal mass and stellar radius causes the crustal
moment of inertia to be more obviously reduced than the total one, eventually
leading to a suppression on the fraction of crustal moment of inertia
$\Delta{I}/I$ in DD-ME$\delta$. The results indicate the crustal moment of
inertia as a more sensitive probe of the neutron-star matter EOS than the total
one, and demonstrate that the isovector scalar meson-nucleon couplings in the
RMF theory could exert influence over the physics of pulsar glitches.
