  As it is known various dynamical processes can be modeled through the systems
of time-fractional order pseudo-differential equations. In the modeling process
one frequently faces with determining the adequate orders of time-fractional
derivatives in the sense of Riemann-Liouville or Caputo. This problem is
qualified as an inverse problem. The right (vector) order can be found
utilizing the available data. In this paper we consider this inverse problem
for linear systems of fractional order pseudo-differential equations. We prove
that the Fourier transform of the vector-solution $\widehat{U}(t, \xi)$
evaluated at a fixed time instance, which becomes possible due to the available
data, recovers uniquely the unknown vector-order of the system of governing
pseudo-differential equations.
