TY - JOUR A1 - Diethelm, Kai A1 - Thai, Ha Duc A1 - Tuan, Hoang The T1 - Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems T2 - Fractional Calculus and Applied Analysis N2 - 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 carefully chosen 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. KW - non-commensurate fractional order planar systems KW - asymptotic behaviour of solutions Y1 - 2022 UR - https://opus4.kobv.de/opus4-fhws/frontdoor/index/index/docId/2230 SN - 1314-2224 VL - 25 SP - 1324 EP - 1360 ER -