  A new class of cosmological models in $f(R, T)$ modified theories of gravity
proposed by Harko et al. (2011), where the gravitational Lagrangian is given by
an arbitrary function of Ricci scalar $R$ and the trace of the stress-energy
tensor $T$, have been investigated for a specific choice of $f(R, T) = f_{1}(R)
+ f_{2}(T)$ by considering time dependent deceleration parameter. The concept
of time dependent deceleration parameter (DP) with some proper assumptions
yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(\alpha t)$, where
$n$ and $\alpha$ are positive constants. For $0 < n \leq 1$, this generates a
class of accelerating models while for $n > 1$, the models of universe exhibit
phase transition from early decelerating phase to present accelerating phase
which is in good agreement with the results from recent astrophysical
observations. Our intention is to reconstruct $f(R,T)$ models inspired by this
special law for the deceleration parameter in connection with the theories of
modified gravity. In the present study we consider the cosmological constant
$\Lambda$ as a function of the trace of the stress energy-momentum-tensor, and
dub such a model "$\Lambda(T)$ gravity" where we have specified a certain form
of $\Lambda(T)$. Such models may display better uniformity with the
cosmological observations. The statefinder diagnostic pair $\{r,s\}$ parameter
has been embraced to characterize different phases of the universe. We also
discuss the physical consequences of the derived models.
