  The inverse problem of determining the order of the fractional Riemann-
Liouville derivative with respect to time in the subdi_usion equation with an
arbitrary positive self-adjoint operator having a discrete spectrum is
considered. Using the classical Fourier method it is proved, that the value of
the norm jju(t)jj of the solution at a_xed time instance recovers uniquely the
order of derivative. A list of examples is discussed, including a linear system
of fractional di_erential equations, di_erential models with involution,
fractional Sturm-Liouville operators, and many others.
