  In this paper, we study two different models of dark energy based on
Chaplygin gas equation of state. The first model is the variable modified
Chaplygin gas while the second one is the extended Chaplygin gas. Both models
are considered in the framework of higher order $f(R)$ modified gravity. We
also consider the case of time varying gravitational constant $G$ and $\Lambda$
for both models. We investigate some cosmological parameters such as the
Hubble, the deceleration and the equation of state parameters. Then we showed
that the model that we considered, extended Chaplygin gas with time-dependent
$G$ and $\Lambda$, is consistent with the observational data. Finally we
conclude with the discussion of cosmological perturbations of our model.
