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Einstein-dilaton-$U(2)$ gauge field theory is considered in a spacetimecharacterised by $\alpha$ and $z$, which are the hyperscaling violation factorand the dynamical critical exponent respectively. We obtain the critical valuesof chemical potential $\mu_c$ that is defined on its boundary dual fluid andderives phase transition from spatially isotropic to anisotropic phase for thevarious values of the $\alpha$ and $z$. To do so, we first applySturm-Liouville theory and estimate the upper bounds of the critical values ofthe 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-Liouvillemethod correctly estimates the critical values of the chemical po10 percenterror ranges. Finally, we compute free energy density of the dual fluid byusing its gravity dual and check if the system shows phase transition at thecritical values of the chemical potential $\mu_c$ for the given parameterregion of $\alpha$ and $z$. Interestingly, it is observed that the anisotropicphase is more favoured than the isotropic phase for small values of $z$ and$\alpha$. However, for large values of $z$ and $\alpha$, the anisotropic phaseis not favoured.tential. It turns out that the two methods are agreed within

Phase transition in anisotropic holographic superfluids with arbitrary $z$ and $\alpha$