  Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$
of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the
Verdier's quotient category to get a relative derived category, where he
localized with respect to $F$-acyclic complexes. In this paper, the homological
properties of relative derived categories are discussed, and the relation with
derived categories is given. For Artin algebras, using relatively derived
categories, we give a relative version on derived equivalences induced by
$F$-tilting complexes. We discuss the relationships between relative
homological dimensions and relative derived equivalences.
