Higher derivative corrections of $f(R)$ gravity with varying equation of state in the case of variable $G$ and $\mathrm{\Lambda }$

In this paper, we study three models of f® modified gravity including higher order terms based on different equation of state parameter. We also assume variable G and $\mathrm{\Lambda }$. By using numerical analysis, we obtain the behavior of some important cosmological parameters, like the Hubble expansion H parameter and the deceleration parameter q. The statefinder diagnostics is also performed for all models.