  Inspired by some recent works of Lovelock Brans-Dicke gravity and mimetic
gravity, cosmology solutions in extensions of these two modified gravities are
investigated. A non-local term is added to the Lovelock Brans-Dicke action and
Gauss-Bonnet terms to the mimetic action,correspondingly. De Sitter and power
scale factor solutions are then obtained in both theories. They can provide
natural new approaches to a more accurate description of the unverse evolution.
