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In recent years, much attention has been paid to the study of forward andinverse problems for the Rayleigh-Stokes equation in connection with theimportance of this equation for applications. This equation plays an importantrole, in particular, in the study of the behavior of certain non-Newtonianfluids. The equation includes a fractional derivative of order $\alpha$, whichis used to describe the viscoelastic behavior of the flow. In this paper, westudy 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.

Inverse problem of determining the order of the fractional derivative in the Rayleigh-Stokes equation