Analysis with observational constraints in $ \Lambda $-cosmology in $f(R,T)$ gravity

An exact cosmological solution of Einstein field equations (EFEs) is derived for a dynamical vacuum energy in $f(R,T)$ gravity for Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time. A parametrization of the Hubble parameter is used to find a deterministic solution of EFE. The cosmological dynamics of our model is discussed in detail. We have analyzed the time evolution of physical parameters and obtained their bounds analytically. Moreover, the behavior of these parameters are shown graphically in terms of redshift $`z'$. Our model is consistent with the formation of structure in the Universe. The role of the $f(R,T)$ coupling constant $\lambda$ is discussed in the evolution of the equation of state parameter. The statefinder and Om diagnostic analysis is used to distinguish our model with other dark energy models. The maximum likelihood analysis has been reviewed to obtain the constraints on the Hubble parameter $H_0$ and the model parameter $n$ by taking into account the observational Hubble data set $H(z)$, the Union 2.1 compilation data set $SNeIa$, the Baryon Acoustic Oscillation data $BAO$, and the joint data set $H(z)$ + $SNeIa$ and $H(z)$ + $SNeIa$ + $BAO$. It is demonstrated that the model is in good agreement with various observations.