Parametrizations of Dark Energy Models in the Background of General Non-canonical Scalar Field in $D$-dimensional Fractal Universe

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.