  Fast Radio Bursts (FRBs) are millisecond-duration pulses occurring at
cosmological distances that have emerged as prominent cosmological probes due
to their dispersion measure (DM) evolution with redshift. In this work, we use
cosmography, a model-independent approach to describe the evolution of the
universe, to introduce the cosmographic expansion of the DM-z relation. By
fitting two different models for the intergalactic medium and host
contributions to a sample of 23 well-localized FRBs, we estimate the kinematic
parameters $q_0=-0.59 \substack{+0.20 \\ -0.17}$, $j_0=1.08 \substack{+0.62 \\
-0.56}$, $s_0=-2.1\pm7.0$, and $H_0=69.4\pm4.7$ achieving a precision of $6\%$
and $7\%$ for the Hubble constant depending on the models used for
contributions. Furthermore, we demonstrate that this approach can be used as an
alternative and complementary cosmological-model independent method to revisit
the long-standing "Missing Baryons" problem in astrophysics by estimating that
$82\%$ of the baryonic content of the universe resides in the intergalactic
medium, within $7\%$ and $8\%$ precision, according to the contribution models
considered here. Our findings highlight the potential of FRBs as a valuable
tool in cosmological research and underscore the importance of ongoing efforts
to improve our understanding of these enigmatic events.
