  In the present work, we investigate some exact cosmological models in the
Myrzakulov $F(R,Q)$ gravity or the Myrzakulov gravity-II (MG-II) which was
proposed in [arXiv:1205.5266]. Here $R$ and $Q$ are the curvature and
nonmetricity scalars using non-special connection, respectively. We have solved
field equations in two different contexts using a flat FLRW metric. We have
obtained two exact solutions in the form of scale factor $a(t)$, and using this
scale factor, we have derived other cosmological parameters. After that using
recent observational datasets $H(z)$ and Pantheon SNe Ia, we have obtained best
fit constrained values of model parameters by applying the MCMC analysis. Using
these best fit values of model parameters, we have discussed the results
behaviour of the derived models. We have found that both models are transit
phase model and approaches to $\Lambda$CDM model at late-time universe. We have
found that the geometrical sector dark equation of state $\omega_{(geom)}$
behaves just like dark energy candidate. Also, we have estimated the transition
redshift $z_{t}$ and present age of the universe $t_{0}$ which are consistent
with recent observations.
