  We explore non-canonical scalar field model in the background of non-flat
$D$-dimensional fractal Universe with cosmological constant $\Lambda$ on the
condition that the matter and scalar field are separately conserved. The
potential $V$, scalar field $\phi$, function $f$, densities, Hubble parameter
and deceleration parameter can be expressed in terms of the redshift $z$ and
these depend on the equation of state parameter $w_{\phi}$. We also investigate
four kinds of well known parametrization models and graphically we have
analyzed the natures of potential, scalar field, function $f$, densities, the
Hubble parameter and deceleration parameter. As a result, the best fitted
values of the unknown parameters ($w_{0},w_{1}$) of the parametrizations models
due to the joint data analysis (SNIa+BAO+CMB+Hubble) are found. Furthermore,
the minimum values of $\chi^{2}$ function are obtained. Also we have plotted
the graphs for different confidence levels 66\%, 90\% and 99\% contours for
($w_{0},~w_{1}$) by fixing the other parameters.
