  We utilise the phenomenologically parameterized piecewise polytropic
equations of state to study various neutron star properties. We investigate the
compliance of these equations of state with several astronomical observations.
We also demonstrate that the theoretical estimates of the fractional moment of
inertia cannot explain all the pulsar glitches observed. We model the crust as
a solid spheroidal shell to calculate the fractional moment of inertia of
fast-spinning neutron stars. We also show that the braking index obtained in a
simple magnetic dipole radiation model with a varying moment of inertia
deviates significantly from the observed data. Future developments in both
theory and observations may allow us to use the fractional moment of inertia
and braking index as observational constraints for neutron star equation of
state.
