  We consider several generalizations of the classical $\gamma$-positivity of
Eulerian polynomials (and their derangement analogues) using generating
functions and combinatorial theory of continued fractions. For the symmetric
group, we prove an expansion formula for inversions and excedances as well as a
similar expansion for derangements. We also prove the $\gamma$-positivity for
Eulerian polynomials for derangements of type $B$. More general expansion
formulae are also given for Eulerian polynomials for $r$-colored derangements.
Our results answer and generalize several recent open problems in the
literature.
