  Nojiri \& Odintsov \cite{noj1} and Hu \& Sawicki \cite{hu} have studied
non-linear functions in modified gravity that explain the cosmic acceleration
without cosmological constant, fulfil the conditions of local gravity \&
stability and pass the solar system tests. In this paper, FRW model, a best
fitted and fruitful mathematical model of the physical universe \cite{rob, hub,
alph, pen} is studied in the context of these non-linear functions. The
cosmological implications such as Hubble parameter, deceleration parameter,
jerk parameter, matter density and the effective equation of state parameter of
the universe are plotted with respect to redshift. Subsequently, the age of the
universe is predicted in $f(R)$ gravity. All are found to represent the
features of present phase of the universe.
