f(R) scalar-tensor cosmology by Noether symmetry

In the framework of f(R) scalar-tensor cosmology, we use the Noether symmetry approach to find the cosmological models consistent with the Noether symmetry. We obtain the functions f(R) and H(a), or the corresponding differential equations, according to specific choices for the scalar field potential V(\phi), the Brans-Dicke function \omega(\phi), some cosmological parameters, and the constants of motion.