  Considering the condition on conservation of energy momentum tensor (EMT), we
study late time cosmological solutions in the context of $f(R,T)=R+\alpha
T^{n}$ gravity (where $\alpha$ and $n$ are constants) in a flat FLRW spacetime.
The present model discusses the case of a barotropic perfect fluid as the
matter content of the Universe, along with the case when dissipative effects
are taken into account. Briefly, assuming a single perfect fluid we find that
the mentioned model is not capable of presenting an observationally consistent
picture of the late time accelerated expansion of the Universe; nevertheless,
the model leads to admissible solutions when the bulk viscosity is included. In
this regard, a consistent setting is found considering the Eckart, Truncated
and Full Israel-Stewart theories which determine the behavior of bulk
viscosity. In the presence of bulk viscosity, the behavior of the deceleration
parameter (DP) shows that the underlying model can describe an acceptable
evolution even if the isotropic pressure of matter content of the Universe is
negligible.
