F(R) cosmology via Noether symmetry and Λ-Chaplygin Gas like model

In this work, we consider f(R) alternative theories of gravity with an eye to Noether symmetry through the gauge theorem. For non-vacuum models, one finds Λ like gravity with energy density of Chaplygin Gas. We also obtain the effective equation of state parameter for corresponding cosmology and scale factor behavior with respect to cosmic time which show that the model provides viable EoS and scale factor with respect to observational data.