  To find more deliberate f(R,T) cosmological solutions, we proceed our
previous paper further by studying some new aspects of the considered models
via investigation of some new cosmological parameters/quantities to attain the
most acceptable cosmological results. Our investigations are performed by
applying the dynamical system approach. We obtain the cosmological
parameters/quantities in terms of some defined dimensionless parameters that
are used in constructing the dynamical equations of motion. The investigated
parameters/quantities are the evolution of the Hubble parameter and its
inverse, the "weight function", the ratio of the matter density to the dark
energy density and its time variation, the deceleration, the jerk and the snap
parameters, and the equation-of-state parameter of the dark energy. We
numerically examine these quantities for two general models $R+\alpha
R^{-n}+\sqrt{-T}$ and $R\log{[\alpha R]}^{q}+\sqrt{-T}$. All considered models
have some inconsistent quantities (with respect to the available observational
data), except the model with n=-0.9 which has more consistent quantities than
the other ones. By considering the ratio of the matter density to the dark
energy density, we find that the coincidence problem does~not refer to a unique
cosmological event, rather, this coincidence also occurred in the early
universe. We also present the cosmological solutions for an interesting model
$R+c_{1}\sqrt{-T}$ in the non--flat FLRW metric. We show that this model has an
attractor solution for the late times, though with $w^{(\textrm{DE})}=-1/2$.
This model indicates that the spatial curvature density parameter gets
negligible values until the present era, in which it acquires the values of the
order $10^{-4}$ or $10^{-3}$. As the second part of this work, we consider the
weak-field [It continues ...]
