  In this paper we study the cosmic acceleration for five dynamical dark energy
models whose equation of state varies with redshift. The cosmological
parameters of these models are constrained by performing a MCMC analysis using
mainly gas mass fraction, $f_{gas}$, measurements in two samples of galaxy
clusters: one reported by Allen et al. (2004), which consists of $42$ points
spanning the redshift range $0.05<z<1.1$, and the other by Hasselfield et al.
(2013) from the Atacama Cosmology Telescope survey, which consists of $91$ data
points in the redshift range $0.118 < \mathrm{z} < 1.36$. In addition, we
perform a joint analysis with the measurements of the Hubble parameter $H(z)$,
baryon acoustic oscillations and the cosmic microwave background radiation from
WMAP and Planck measurements to estimate the equation of state parameters. We
obtained that both $f_{gas}$ samples provide consistent constraints on the
cosmological parameters. We found that the $f_{gas}$ data is consistent at the
$2\sigma$ confidence level with a cosmic slowing down of the acceleration at
late times for most of the parameterizations. The constraints of the joint
analysis using WMAP and Planck measurements show that this trend disappears. We
have confirmed that the $f_{gas}$ probe provides competitive constraints on the
dark energy parameters when a $w(z)$ is assumed.
