Abstract
Abstract We investigated f(R) gravity with k-essence using the Starobinsky model as an example, given by the expression f(R) = R + α R 2. Using the hybrid function of the scale factor, we found the scalar field function and its potential. For the model under consideration, the parameters of the slow roll-off satisfy the inflationary stage. Our model allows us to obtain an accelerated expansion of the Universe during an inflationary period. A non-uniform non-viscous fluid was investigated, and then the viscosity was introduced in the second example. Received fluid equations for the accelerated universe.