  We study a cosmological model in Rastall's theory of gravity in the framework
of the flat FLRW metric. We formulate the value of the Hubble parameter, which
contains two model parameters, $ \alpha $ and $ j $. Employing the Markov Chain
Monte Carlo (MCMC) sampling technique, we determine the values of these model
parameters along with their uncertainties. Moreover, we derive the equation of
state (EoS) parameter, which converges around the quintessence region. We
perform a dynamical system analysis using the linearization technique to
validate the results independently. Also, we discuss various physical
attributes of the model, highlighting the transition to acceleration and the
violation of the strong energy condition (SEC) in the late stages of evolution.
In conclusion, our model mimics the behavior of a dark matter fluid during the
past epoch and transitions into a quintessence dark energy model in the future
epoch.
