  Some new exact solutions of Einstein's field equations have come forth within
the scope of a spatially homogeneous and anisotropic Bianchi type-III
space-time filled with barotropic fluid and dark energy by considering a
variable deceleration parameter. We consider the case when the dark energy is
minimally coupled to the perfect fluid as well as direct interaction with it.
Under the suitable condition, the anisotropic models approach to isotropic
scenario. We also find that during the evolution of the universe, the equation
of state (EoS) for dark energy $\omega^{(de)}$, in both cases, tends to -1
(cosmological constant, $\omega^{(de)} = -1$), by displaying various patterns
as time increases, which is consistent with recent observations. The cosmic
jerk parameter in our derived models are in good agreement with the recent data
of astrophysical observations under appropriate condition. It is observed that
the universe starts from an asymptotic Einstein static era and reaches to the
$\Lambda$CDM model. So from recently developed Statefinder parameters, the
behavior of different stages of the universe has been studied. The physical and
geometric properties of cosmological models are also discussed.
