Conformal equivalence and Noether symmetries in cosmology

In this paper, we discuss a possible method of finding cosmological exact solutions in the context of nonstandard coupled gravity theories. We consider whether Noether symmetries, present in the cosmological 'point-like' Lagrangian, are preserved under the conformal transformation which reduces a given nonstandard coupled model to the corresponding standard coupled one. We see that Noether symmetries are conformally preserved in a general way.