Bianchi type-III, V, and VI0 perfect fluid anisotropic cosmological models have been discussed in the theory of gravity suggested by [T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, f(R, T) gravity, Phys. Rev. D 84 (2011) 024020] with two well-known functional forms, namely, [Formula: see text] and [Formula: see text], here [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are constants. To acquire the solutions of the field equations of the three models, the average scale factor and the proportionality of expansion scalar with shear scalar are used. The behavior of all the physical and geometrical properties of the three models is explained with their plots. For all the three models, the NEC is positive, which implies that the EoS parameter is in the quintessence region. For the Bianchi type-III model, the SEC is violated, which recommends that the present universe is accelerating and expanding. Also, we have observed that, if [Formula: see text], [Formula: see text], and [Formula: see text], then the two functional forms lead to the linear form and for [Formula: see text], the second form leads to the quadratic form, these two are interesting points in this paper. It can be observed that the stability analysis of the obtained models background solutions is discussed through perturbation techniques and observed that the background solutions are stable. The values of all the parameters in the three models match with the recent cosmological observations.