Modeling cosmic acceleration with a generalized varying deceleration parameter

Understanding the accelerating expansion of the Universe remains a fundamental challenge in modern cosmology. In this paper, we investigate a cosmological model parametrized by a generalized variable deceleration parameter to elucidate the dynamics driving cosmic acceleration. By employing constraints from the latest observational datasets, including Cosmic Chronometers (CC), Type Ia Supernovae (SNe), and Baryon Acoustic Oscillations (BAO), we assess the compatibility of the model with observational data. The chosen parametrization aligns with thermodynamic constraints on the deceleration parameter, further validating its reliability. Further, we estimate the present value of the Hubble parameter, transition redshift, deceleration parameter, and EoS parameter, which align with observational data. Lastly, our stability analysis confirms the model's stability against small perturbations.