  Since the discovery of cosmic acceleration, modified gravity theories play an
important role in the modern cosmology. In particular, the well-known F(R) -
theories reached great popularity motivated by the easier formalism and by the
prospect to find a final theories of gravity for the dark scenarios. In the
present work, we study some generalizations of F(R), F(T) and F(Q) gravity
theories, where $R, T, Q$ are the Ricci, torsion and nonmetricity scalars. At
the beginning, we briefly review the formalism of such theories. Then, we will
consider one of their generalizations, the so-called Myrzakulov F(R,T) gravity
theory or the MG-I theory. The point-like Lagrangian is explicitly presented.
Based on this Lagrangian, the field equations of MG-I are found. For the
specific model $F(R,T)=\mu R+\nu T,$ the corresponding exact solutions are
derived. Furthermore, we will consider the physical quantities associated to
such solutions and we will find how for some values of the parameters the
expansion of our universe can be accelerated without introducing any dark
component. Finally, some metric-affine Myrzakulov gravity theories with and
without boundary term scalars are presented.
