  Motivated by UV completion of general relativity with a modification of a
geometry at high energy scale, it is expected to have an energy dependent
geometry. In this paper, we introduce charged black hole solutions with power
Maxwell invariant source in the context of gravity's rainbow. In addition, we
investigate two classes of $F(R)$ gravity's rainbow solutions. At first, we
study energy dependent $F(R)$ gravity without energy momentum tensor, and then
we obtain $F(R)$ gravity's rainbow in the presence of conformally invariant
Maxwell source. We study geometrical properties of the mentioned solutions and
compare their results. We also give some related comments regarding to
thermodynamical behavior of the obtained solutions and discuss thermal
stability of the solutions.
