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)].
An outbreak of the novel coronavirus disease was first reported in Wuhan, China in December 2019. In India, the first case was reported on January 30, 2020 on a person with a travel history to an affected country. Considering the fact of a heavily populated and diversified country like India, we have proposed a novel fractional-order mathematical model to elicit the transmission dynamics of the coronavirus disease (COVID-19) and the control strategy for India. The classical SEIR model is employed in three compartments, namely: quarantined immigrated population, non-quarantined asymptomatic immigrated population, and local population subjected to lockdown in the containment areas by the government of India to prevent the spread of disease in India. We have also taken into account the physical interactions between them to evaluate the coronavirus transmission dynamics. The basic reproduction number ($R_{0}$) has been derived to determine the communicability of the disease. Numerical simulation is done by using the generalised Euler method. To check the feasibility of our analysis, we have investigated some numerical simulations for various fractional orders by varying values of the parameters with help of MATLAB to fit the realistic pandemic scenario.
In this paper, we present two viscous models of non-perfect fluid by avoiding the introduction of exotic dark energy. We consider the first model in terms of deceleration parameter [Formula: see text] has a viscosity of the form [Formula: see text] and the other model in quadratic form of [Formula: see text] of the type [Formula: see text]. In this framework we find the solutions of field equations by using inhomogeneous equation of state of form [Formula: see text] with equation of state parameter [Formula: see text] is constant and [Formula: see text].
In this paper an attempt has been made to study the flat fractal Friedmann–Robertson–Walker model filled with domain walls. We have obtained the fractal equation of deceleration parameter and tension of the domain wall. It is observed that, while domain walls exist at early times, they disappear at late time. Finally, some physical parameters of the model are discussed using graphs.
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