Asymptotic stability of linear fractional systems with constant coefficients and small time dependent perturbations

TL;DR

This paper studies how small time-dependent perturbations affect the long-term stability of solutions in linear fractional differential systems, showing stability preservation under certain conditions.

Contribution

It demonstrates that asymptotic stability of linear fractional systems is maintained despite small nonautonomous perturbations, extending stability results to perturbed fractional systems.

Findings

Asymptotic stability is preserved under small perturbations.

Stability results apply to both linear and nonlinear perturbations.

The analysis extends classical stability theory to fractional systems.

Abstract

Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of small (either linear or nonlinear) nonautonomous perturbations the trivial solution of the perturbed system is also asymptotically stable.