  Einstein-dilaton-$U(2)$ gauge field theory is considered in a spacetime
characterised by $\alpha$ and $z$, which are the hyperscaling violation factor
and the dynamical critical exponent respectively. We obtain the critical values
of chemical potential $\mu_c$ that is defined on its boundary dual fluid and
derives phase transition from spatially isotropic to anisotropic phase for the
various values of the $\alpha$ and $z$. To do so, we first apply
Sturm-Liouville theory and estimate the upper bounds of the critical values of
the chemical potential. We also employ a numerical method in the ranges of $1
\leq z \leq 4$ and $0 \leq \alpha \leq 4$ to check if the Sturm-Liouville
method correctly estimates the critical values of the chemical po10 percent
error ranges. Finally, we compute free energy density of the dual fluid by
using its gravity dual and check if the system shows phase transition at the
critical values of the chemical potential $\mu_c$ for the given parameter
region of $\alpha$ and $z$. Interestingly, it is observed that the anisotropic
phase is more favoured than the isotropic phase for small values of $z$ and
$\alpha$. However, for large values of $z$ and $\alpha$, the anisotropic phase
is not favoured.tential. It turns out that the two methods are agreed within
