  The cosmic acceleration observed in the expansion of the Universe has sparked
extensive research into the nature of dark energy, which is known to constitute
approximately 70\% of the Universe's energy content. In this study, we explore
two parametrizations of the Hubble parameter, namely power-law and logarithmic
corrections, as alternatives to the standard $\Lambda$CDM model. Using
observational data from Cosmic Chronometers (CC), Pantheon+, and the Baryonic
Acoustic Oscillations (BAO) datasets, we investigate the dynamics of essential
cosmological parameters, including the deceleration parameter, energy density,
pressure, and equation of state (EoS) parameter. The $Om(z)$ diagnostic test is
employed to classify different dark energy models. Our cosmological models,
with the power-law and logarithmic corrections, are found to provide a good fit
to the recent observational data and efficiently describe the cosmic expansion
scenario.
