A universe media is considered as a bulk viscosity described by inhomogeneous equation of state (EOS) of the form [Formula: see text], where [Formula: see text] is a time-dependent parameter. A generalized dynamical equation for the scale factor of the universe is proposed to describe the cosmological evolution, in which we assume the bulk viscosity and time-dependent parameter [Formula: see text] are linear combination of two terms of the form: [Formula: see text] and [Formula: see text], i.e.[Formula: see text]one is constant and other is proportional to Hubble parameter [Formula: see text]. In this framework, we demonstrate that this model can be used to explain the dark energy dominated universe, and the inhomogeneous term of specific form introduced in EOS, may lead to three kinds of fates of cosmological evolution: no future singularity, big rip or Type[Formula: see text]III singularity as presented by [S. Nojiri and S. D. Odintsov, Phys. Rev. D 72, 023003 (2005)].

In this paper we have obtained the exact solution of the Einstein field equations by using global equation of state of the form p = 1 3 ρφ, where φ is a function of the scale factor R for Zeldovich fluid satisfying G = G 0 (R R0) m. We also studied the two variable Λ model, viz. Λ ∼ (Ṙ R) 2 and Λ ∼ ρ under the assumption that the equation of state parameter ω is time-dependent i.e. ω = ω(t) in the framework of Kaluza-Klein theory of gravitation.