  We consider the quasi-stationary distribution of the classical Shiryaev
diffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$.
We derive analytically a closed-form formula for the distribution's fractional
moment of an {\em arbitrary} given order $s\in\mathbb{R}$; the formula is
consistent with that previously found by Polunchenko and Pepelyshev (2018) for
the case of $s\in\mathbb{N}$. We also show by virtue of the formula that, if
$s<1$, then the $s$-th fractional moment of the quasi-stationary distribution
becomes that of the exponential distribution (with mean $1/2$) in the limit as
$A\to+\infty$; the limiting exponential distribution is the stationary
distribution of the reciprocal of the Shiryaev diffusion.
