ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Asymptotic Stability of Fractional Langevin Systems

Journal of Applied Nonlinear Dynamics 11(3) (2022) 635--650 | DOI:10.5890/JAND.2022.09.008

Venkatesan Govindaraj$^1$, Sivaraj Priyadharsini$^2$, Pitchaikkannu Suresh Kumar$^3$, Krishnan Balachandan$^4$

$^1$ Department of Mathematics, National Institute of Technology Puducherry, Karaikkal - 609 609, India

$^2$ Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore - 641 008, India

$^3$ Department of Mathematics, National Institute of Technology, Calicut - 673 601, India

$^4$ Department of Mathematics, Bharathiar University, Coimbatore - 641 046, India

Abstract

In the paper, we present a method based on eigenvalue criterion to test the asymptotic stability of fractional linear Langevin systems represented by the fractional differential equation in the sense of Caputo fractional derivative. Also, this method is extended to nonlinear equations and finally some sufficient conditions ensuring asymptotical stability of fractional-order nonlinear Langevin systems are proposed. Some numerical examples are provided to illustrate the effectiveness of the proposed method.

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