In this work, we study the late-time cosmological solutions of f(R,T)=g(R)+h(−T) models assuming that the conservation of the energy-momentum tensor (EMT) is violated. We perform our analysis through constructing an autonomous dynamical system for the equations of motion. We study the stability properties of solutions via considering linear perturbations about the related equilibrium points. Moreover, we parameterize the Lagrangian by introducing the parameters m(r) and n(s). These parameters which are constructed out of the functions g(R) and h(−T) play the main role in finding the late-time behavior of the solutions. We find that there exist, in general, three classes of solutions, all models with n>0 include a proper transition from a prolonged matter era to a de Sitter solution. Models with −0.51 , for at least a root of equation n(s)=s−1 , include an unphysical dark energy solution preceding an improper matter era. Finally, for n<−1/2 there is a transient accelerated expansion era with −1/2
