  In this work, we have made a systematic study of how the gravitational wave
frequency of the fundamental mode from compact stars is affected by anisotropic
effects using realistic equations of state. Our study is an extension of the
seminal research performed by Doneva [Phys. Rev. D 85 (2012) 124023], where a
polytropic equation of state was used. To achieve our objective, we considered
compact stars which were built by using equations of state in the framework of
a relativistic mean field theory for the case of hadronic stars and in the
framework of the MIT model for the case of quark stars. In order to obtain some
pertinent information that could give us the possibility to detect the
anisotropy in compact stars, we also studied and analized the behaviour of
various global stellar quantities, e.g., gravitational redshift, stellar mass,
radius, among others. We concluded that the anisotropic effects can have
important consequences, which are strongly related to the anisotropic parameter
and the equation of state of high density matter. Additionally, a comparison
with observational data has been made and we have shown that the anisotropic
parameter $\lambda$ can be used as a tuning parameter to reproduce mass and
radius observational data of neutron stars.
