  We consider $f(R, T)$ theory of gravity, where $R$ is the curvature scalar
and $T$ the trace of the energy momentum tensor. Attention is attached to the
special case, $f(R, T)= R+2f(T)$ and two expressions are assumed for the
function $f(T)$, $\frac{a_1T^n+b_1}{a_2T^n+b_2}$ and $a_3\ln^{q}{(b_3T^m)}$,
where $a_1$, $a_2$, $b_1$, $b_2$, $n$, $a_3$, $b_3$, $q$ and $m$ are input
parameters. We observe that by adjusting suitably these input parameters,
energy conditions can be satisfied. Moreover, an analyse of the perturbations
and stabilities of de Sitter solutions and power-law solutions is performed
with the use of the two models. The results show that for some values of the
input parameters, for which energy conditions are satisfied, de Sitter
solutions and power-law solutions may be stables.
