  This paper is devoted to studying the asymptotic behaviour of solutions to
generalized non-commensurate fractional systems. To this end, we first consider
fractional systems with rational orders and introduce a criterion that is
necessary and sufficient to ensure the stability of such systems. Next, from
the fractional-order pseudospectrum definition proposed by \v{S}anca et al., we
formulate the concept of a rational approximation for the fractional spectrum
of a noncommensurate fractional systems with general, not necessarily rational,
orders. Our first important new contribution is to show the equivalence between
the fractional spectrum of a noncommensurate linear system and its rational
approximation. With this result in hand, we use ideas developed in our earlier
work to demonstrate the stability of an equilibrium point to nonlinear systems
in arbitrary finite-dimensional spaces. A second novel aspect of our work is
the fact that the approach is constructive. Finally, we give numerical
simulations to illustrate the merit of the proposed theoretical results.
