  In the present paper, we investigate some exact cosmological models in
Myrzakulov $F(R,T)$ gravity theory. We have considered the arbitrary function
$F(R, T)=R+\lambda T$ where $\lambda$ is an arbitrary constant, $R, T$ are
respectively, the Ricci-scalar curvature and the torsion. We have solved the
field equations in a flat FLRW spacetime manifold for Hubble parameter and
using the MCMC analysis, we have estimated the best fit values of model
parameters with $1-\sigma, 2-\sigma, 3-\sigma$ regions, for two observational
datasets like $H(z)$ and Pantheon SNe Ia datasets. Using these best fit values
of model parameters, we have done the result analysis and discussion of the
model. We have found a transit phase decelerating-accelerating universe model
with transition redshifts $z_{t}=0.4438_{-0.790}^{+0.1008},
0.3651_{-0.0904}^{+0.1644}$. The effective dark energy equation of state varies
as $-1\le\omega_{de}\le-0.5176$ and the present age of the universe is found as
$t_{0}=13.8486_{-0.0640}^{+0.1005}, 12.0135_{-0.2743}^{+0.6206}$ Gyrs,
respectively for two datasets.
