  In this paper, we study a spatially homogeneous and isotropic FLRW
cosmological model in framework of the symmetric teleparallel $f(Q)$ gravity
proposed by Jimenez et al. (Physical Review D 98.4 (2018): 044048), where the
non-metricity $Q$ is responsible for the gravitational interaction. For the
whole analysis we have considered a special form of $f\left(Q\right)$ gravity
function i.e. $f\left( Q\right) =\alpha Q^{n}+\beta $ (where $\alpha $, $\beta
$, and $n$ are the dynamical model constant parameters) in the direction of
$t\left( z\right) =\frac{kt_{0}}{b}f\left( z\right)$, where, $f\left( z\right)
=W\left[ \frac{b}{k}e^{\frac{b-\ln \left(1+z\right) }{k}}\right] $ and $W$
denotes the Lambert function. We have discussed two cases of the function:
linear $f(Q)$ model towards $ n=1$ and quadratic for $n=2$. In both the model
we had verified the validity of the models with the help of energy conditions
along with some physical parameters like equation of state parameter, jerk
parameter, statefinder parameters are also discussed in details and compared it
with the observational data.
