Exact solution of the fiels equation of the generalized cosmological F(R,T) model

We considered cosmological model within the framework of the generalized F(R,T) gravityin flat FLRW metric.  Earlier, an exponential solution was shown for the generalized case, which describes the inflationary stage of the evolution of the Universe. In this paper, it is shown that for the particular case of the Starobinsky model, the generalized model has, amongother things, a power-law solution that describes the dust-like stage  and  the  stage  of  radiation  dominance.It  should  be  noted  that  this  solution  was  obtained  by  the  analytical  method  as  a  solution  to  the  Euler-Lagrange  equation  for  this  model,  taking  into  account  the  functions  u,  v–  describing  the  relationship  between  the  curvature  scalar  and  the  torsion  scalar,  and  depending not only on the first, but also on the second time derivative of the scale factor. This solution is of interest, since it shows not only that this model has a solution, but also that this solution can describe the modern observable Universe for more complex forms u, v than described earlier.This solution allows other related cosmological parameters to be obtained accordingly. The paper presents the parameter for the equation of state, which describes the stage of the evolution of the Universe. Keywords:generalized cosmological model, scale factor, Starobinsky model