The present study investigates the Friedmann–Lemaitre–Robertson–Walker models (often FLRW models) with time varying G and \(\Lambda \) in the general theory of relativity. In this communication the Einstein field equations have been solved by considering the deceleration parameter q(t) as a varying function of time t and the Hubble parameter H defined as \(q=-l(t-t_0)+\beta -1\) and \(q=-1+\frac{2\alpha (H-1)}{H}\) , where \(l,t_0,\beta , \alpha \) are non-negative constants. We have analyzed the values of different constants that will generate a transition for the universe from an early decelerating phase to a recent acceleration phase. The physical and graphic behaviour have also been planned to study in this communication.
