# American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021274
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## Stability and applications of multi-order fractional systems

 Department of Electrical Engineering, University of Chile, Av. Tupper 2007, Santiago, Chile

Received  September 2020 Revised  August 2021 Early access November 2021

Fund Project: The author thanks the anonymous reviewers for their comments. This research was supported by CONICYTPCHA/National PhD scholarship program, 2018

This paper establishes conditions for global/local robust asymptotic stability for a class of multi-order nonlinear fractional systems consisting of a linear part plus a global/local Lipschitz nonlinear term. The derivation order can be different in each coordinate and take values in $(0, 2)$. As a consequence, a linearized stability theorem for multi-order systems is also obtained. The stability conditions are order-dependent, reducing the conservatism of order-independent ones. Detailed examples in robust control and population dynamics show the applicability of our results. Simulations are attached, showing the distinctive features that justify multi-order modelling.

Citation: Javier Gallegos. Stability and applications of multi-order fractional systems. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021274
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Robust performance
Population dynamics depending on the derivation order

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