  In this paper we introduce color Hom-Akivis algebras and prove that the
commutator of any color non-associative Hom-algebra structure map leads to a
color Hom-akivis algebra. We give various constructions of color Hom-Akivis
algebras. Next we study flexible and alternative color Hom-Akivis algebras.
Likewise color Hom-Akivis algebras, we introduce non-commutative color
Hom-Leibniz-Poisson algebras and presente several constructions. Moreover we
give the relationship between Hom-dialgebras and Hom-Leibniz-Poisson algebras;
i.e. a Hom-dialgebras give rise to a Hom-Leibniz-Poisson algebra. Finally we
show that twisting a color Hom-Leibniz module structure map by a color
Hom-Leibniz algebra endomorphism, we get another one.
