Аннотация
Abstract Now exist several alternative cosmological models that describe observable properties of our universe. In particular, it is such models as F (R) and F (T ) gravity. We consider properties of their generalization as F (R, T ) model of gravity with kessence. We obtained some exact solutions of particular cass of scale factor a for general formof the F (R, T ) functions with scalar field. These solutions describe the accelerated/deccelerated periods of the universe.