Stability and phase space analysis in f(R) theory with generalized exponential f(R) model

We have studied in this paper, the stability of dynamical system in f(R) gravity. We have considered the f(R) gamma-gravity and explored its dynamical analysis. We found six critical points among which only one describes a universe filled of both matter and dominated dark energy. It is shown that these critical points present specific phase spaces described by the corresponding fluids. Furthermore, we have investigated the stability conditions of these critical points and find that these conditions are dependent of the model parameters. We also study the stability of a new power-law f*(R) model with de Sitter and power law solutions.