baryon number fluctuations especially the ratio of fourth over second order cumulants of baryon number fluctuations to determine $h(\Phi)$. The kurtosis of baryon number fluctuations is given by $\kappa\sigma^2=C_4^B/C_2^B$ with the variance $\sigma^2=C_2^B$ and the kurtosis $\kappa={C_4^B}/{(\sigma^2)^2}$, and the cumulants of baryon number distributions are given by $C_n^B=VT^3\chi^B_n$, where the baryon number susceptibilities are defined as: $$\begin{aligned}
\chi^B_n = \frac{\partial^n[P / T^4]}{\partial[\mu_B / T]^n},\end{aligned}$$ and $P,V$ are the pressure and volume of the system, and $\mu_B=3 \mu$ is the baryon number chemical potential. The calculation of baryon number fluctuations in the holographic QCD model of [@Yang:2014bqa] has been investigated in Ref. [@Li:2017ple]. The baryon number fluctuations in the PNJL model has been investigated in Ref. [@Li:2018ygx] and it is observed that in the PNJL model [@Li:2018ygx] that the ratio of fourth over second order cumulants of net-baryon number fluctuations $\kappa\sigma^2$ at zero baryon number density is dominated by contribution from gluodynamics. Therefore, we fix the chemical potential dependence of the dilaton field by fitting the lattice results of the kurtosis of baryon number fluctuations [@Bazavov2017The] at zero chemical potential.

The kurtosis $\kappa\sigma^2$ as a function of the normalized temperature $T/T_0$ with $T_0=217~{\rm MeV}$ comparing with lattice result [@Bazavov2017The] is shown 