  The impulse response of a generalized fractional second order filter of the
form ${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-\gamma}}$ is derived, where
$0<\alpha \le 1$, $0<\gamma <2$. The asymptotic properties of the impulse
responses are obtained for two cases, and the two cases show the similar
properties for the changing of $\gamma$ values. It is shown that only when
${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-1}}$ has the critical stability, the
generalized fractional second order filter
${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-\gamma}}$ has different properties as
we change the value of $\gamma$. Finally, numerical examples to illustrate the
impulse response are provided to verify the proposed concepts.
