  This paper is devoted to studying non-commensurate fractional order planar
systems. Our contributions are to derive sufficient conditions for the global
attractivity of non-trivial solutions to fractional-order inhomogeneous linear
planar systems and for the Mittag-Leffler stability of an equilibrium point to
fractional order nonlinear planar systems. To achieve these goals, our approach
is as follows. Firstly, based on Cauchy's argument principle in complex
analysis, we obtain various explicit sufficient conditions for the asymptotic
stability of linear systems whose coefficient matrices are constant. Secondly,
by using Hankel type contours, we derive some important estimates of special
functions arising from a variation of constants formula of solutions to
inhomogeneous linear systems. Then, by proposing new weighted norms combined
with the Banach fixed point theorem for appropriate Banach spaces, we get the
desired conclusions. Finally, numerical examples are provided to illustrate the
effect of the main theoretical results.
