  In this study, we construct a theoretical framework based on the generalized
Hubble parameter form which may arise within the particle creation, viscous and
$f(R)$ gravity theory. The Hubble parameter is scrutinized for its
compatibility with the observational data relevant to the late-time universe.
By using Bayesian statistical techniques based on $\chi^{2}$ minimization
method, we determine model parameters's best fit values for the cosmic
chronometer and supernovae Pantheon datasets. For the best fit values, the
cosmographic and physical parameters are analyzed to understand the cosmic
dynamics in model.
