Abstract
A non-minimally coupled cosmological scenario is considered in the context of f(R,T)=f1(R)+f(2)(R)f(3)(T) gravity (with R being the Ricci scalar and T the trace of the energy-momentum tensor) in the background of the flat Friedmann-Robertson-Walker (FRW) model. The field equations of this modified theory are solved using a time-dependent deceleration parameter for a dust. The behavior of the model is analyzed taking into account constraints from recent observed values the deceleration parameter. It is shown that the analyzed models can explain the transition from the decelerating phase to the accelerating one in the expansion of the universe, by staying true to the results of the observable universe. It is shown that the models are dominated by a quintessence-like cosmological dark fluid at the late universe.