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Polytropic and Chaplygin f(R)-gravity models

We reconstruct different f(R)-gravity models corresponding to the polytropic, standard Chaplygin, generalized Chaplygin, modified Chaplygin and modified variable Chaplygin gas dark energy models. We also obtain the equation of state parameters of the corresponding f(R)-gravity models which describe the accelerated expansion of the universe. We conclude that although the equation of state parameters of the obtained f(R)-gravities can behave like phantom or quintessence dark energy models, they cannot justify the transition from the quintessence state to the phantom regime. Furthermore, the polytropic and Chaplygin f(R)-gravity models in de Sitter space can satisfy the inflation condition.