Journal of Applied Nonlinear Dynamics
Asymptotic Stability of Fractional Langevin Systems
Journal of Applied Nonlinear Dynamics 11(3) (2022) 635650  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
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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 fractionalorder nonlinear Langevin systems are proposed. Some numerical examples are provided to illustrate the effectiveness of the proposed method.
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