  This article deals with the initial-boundary value problem for a moderately
coupled system of time-fractional diffusion equations. Defining the mild
solution, we establish fundamental unique existence, limited smoothing property
and long-time asymptotic behavior of the solution, which mostly inherit those
of a single equation. Owing to the coupling effect, we also obtain the
uniqueness for an inverse problem on determining all the fractional orders by
the single point observation of a single component of the solution.
