A note about the linearized stability of a class of nonlinear fractional differential systems

TL;DR

This paper examines the linearized stability of certain nonlinear fractional differential systems of order between 1 and 2, correcting previous inaccuracies and providing a new stability criterion.

Contribution

It corrects existing results on stability and introduces a new criterion for testing asymptotic stability of these fractional systems.

Findings

Some recent stability results are incorrect.

A new criterion for asymptotic stability is proposed.

Clarifies the stability conditions for fractional differential systems.

Abstract

In this paper, we discuss on the linearized stability of the trivial solution for a class of nonlinear Caputo fractional differential systems of order $\alpha\in(1,2)$. We show that some recent existing results in this direction are wrong. To complete the literature we also give a criterion to test the asymptotic stability of the trivial solution of this system.