TY - INPR A1 - Diethelm, Kai A1 - Hashemishahraki, Safoura A1 - Thai, Ha Duc A1 - Tuan, Hoang The T1 - A constructive approach for investigating the stability of incommensurate fractional differential systems N2 - This paper is devoted to studying the asymptotic behaviour of solutions to generalized noncommensurate 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 Sanca 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. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-51954 ER - TY - INPR A1 - Diethelm, Kai A1 - Hashemishahraki, Safoura A1 - Thai, Ha Duc A1 - Tuan, Hoang The T1 - Stability properties of multi-order fractional differential systems in 3D N2 - This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions are for the asymptotic stability of such systems are obtained. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-51960 ER -