  In this paper, we investigate some aspects of the qualitative theory for
multi-order fractional differential equation systems. First, we obtain a
fundamental result on the existence and uniqueness for multi-order fractional
differential equation systems. Next, a representation of solutions of
homogeneous linear multi-order fractional differential equation systems in
series form is provided. Finally, we give characteristics regarding the
asymptotic behavior of solutions to some classes of linear multi-order
fractional differential equation systems.
