  Fast Radio Bursts (FRBs) are millisecond-duration radio transients with an
observed dispersion measure ($DM$) greater than the expected Milky Way
contribution, which suggests that such events are of extragalactic origin.
Although some models have been proposed to explain the physics of the pulse,
the mechanism behind the FRBs emission is still unknown. From FRBs data with
known host galaxies, the redshift is directly measured and can be combined with
estimates of the $DM$ to constrain the cosmological parameters, such as the
baryon number density and the Hubble constant. However, the poor knowledge of
the fraction of baryonic mass in the intergalactic medium ($f_{IGM}$) and its
degeneracy with the cosmological parameters impose limits on the cosmological
application of FRBs. In this work we present a cosmological model-independent
method to determine the evolution of $f_{IGM}$ combining the latest FRBs
observations with localized host galaxy and current supernovae data. We
consider constant and time-dependent $f_{IGM}$ parameterizations and show,
through a Bayesian model selection analysis, that a conclusive answer about the
time-evolution of $f_{IGM}$ depend strongly on the $DM$ fluctuations due to the
spatial variation in cosmic electron density ($\delta$). In particular, our
analysis show that the evidence varies from strong (in favor of a growing
evolution of $f_{IGM}$ with redshift) to inconclusive, as larger values of
$\delta$ are considered.
