Observational tests of \texorpdfstring{$\Lambda(t)$}{Lambda(t)} cosmology in light of DESI DR2

In this article, we investigate two phenomenological decaying vacuum cosmological models describing the accelerated expansion of the Universe. We constrain the model parameters using a Markov Chain Monte Carlo (MCMC) technique with recent datasets, including cosmic chronometer (CC), Pantheon+SH0ES (PPS), and DESI BAO data release (DR2). Our analysis provides constraints from PPS, PPS+CC, and the joint PPS+CC+DR2 datasets for both models. All datasets favor $H_0 \simeq 72.53$--$73.01~\mathrm{Km\,s^{-1}\,Mpc^{-1}}$, while $\Omega_{m0}$ is higher with PPS alone and decreases to standard paradigm estimates with the inclusion of additional data. The evolution parameter is $n \approx 0.30$ from joint analysis, indicating a mild deviation from the $\Lambda$CDM framework. Furthermore, the physical behavior of the models is examined through the deceleration parameter and the total equation of state, confirming a smooth transition from past deceleration expansion to the present accelerated expansion.