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Extragalactic dispersion measures (DMs) obtained from observations of fastradio bursts (FRBs) are an excellent tool for probing intergalactic medium(IGM) and for conducting cosmography. However, the DM contribution from the IGM(${\rm DM_{IGM}}$) depends on the fraction of baryon mass in the IGM, $f_{\rmIGM}$, which is not properly constrained. As $f_{\rm IGM}(z)$ is geometricallyrelated to the Hubble parameter $H(z)$ and ${\rm DM_{IGM}}(z)$, here we proposethat combining two independent measurements of FRBs and $H(z)$ in similarredshift ranges provides a novel and cosmology-free method to constrain theevolution of $f_{\rm IGM}(z)$. Under the assumption that $f_{\rm IGM}$ isevolving with redshift in a functional form, we forecast that the evolution of$f_{\rm IGM}(z)$ can be well inferred in a combined analysis of $\sim3000$${\rm DM_{IGM}}(z)$ derived from FRBs and $\sim50$ $H(z)$ derived from theHubble parameter data. Though the efficiency of our method is not as good asthat of the other model-independent method involving the joint measurements ofDM and luminosity distance of FRBs, our method offers a new model-independentway to constrain $f_{\rm IGM}(z)$.

Constraining the Evolution of the Baryon Fraction in the IGM with FRB and H(z) data