  In recent years, much attention has been paid to the study of forward and
inverse problems for the Rayleigh-Stokes equation in connection with the
importance of this equation for applications. This equation plays an important
role, in particular, in the study of the behavior of certain non-Newtonian
fluids. The equation includes a fractional derivative of order $\alpha$, which
is used to describe the viscoelastic behavior of the flow. In this paper, we
study the behavior of the solution of such equations depending on the parameter
$\alpha$. In particular, it is proved that for sufficiently large $t$ the norm
$||u(x,t)||_{L_2(\Omega)}$ of the solution decreases with respect to $\alpha$.
Moreover the inverse problem of determining the order of the derivative
$\alpha$ is solved uniquely.
