Stability of a Nonlinear Fractional Langevin System with Nonsingular Exponential Kernel and Delay Control
Open Access
- 3 November 2022
- journal article
- research article
- Published by Hindawi Limited in Discrete Dynamics in Nature and Society
- Vol. 2022, 1-16
- https://doi.org/10.1155/2022/9169185
Abstract
Fractional Langevin system has great advantages in describing the random motion of Brownian particles in complex viscous fluid. This manuscript deals with a delayed nonlinear fractional Langevin system with nonsingular exponential kernel. Based on the fixed point theory, some sufficient criteria for the existence and uniqueness of solution are established. We also prove that this system is UH- and UHR-stable attributed to the nonlinear analysis and inequality techniques. As applications, we provide some examples and simulations to illustrate the availability of main findings.Keywords
Funding Information
- Taizhou University
This publication has 39 references indexed in Scilit:
- Caputo-Fabrizio Derivative Applied to Groundwater Flow within Confined AquiferJournal of Engineering Mechanics, 2017
- Stability of nonlocal fractional Langevin differential equations involving fractional integralsJournal of Applied Mathematics and Computing, 2016
- Revisited Fisher’s equation in a new outlook: A fractional derivative approachPhysica A: Statistical Mechanics and its Applications, 2015
- Analysis of the Keller–Segel Model with a Fractional Derivative without Singular KernelEntropy, 2015
- Langevin equation for a free particle driven by power law type of noisesPhysics Letters A, 2014
- Laplace transform and Hyers–Ulam stability of linear differential equationsJournal of Mathematical Analysis and Applications, 2013
- GENERALIZED ULAM–HYERS STABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONSInternational Journal of Mathematics, 2012
- Fractional generalized Langevin equation approach to single-file diffusionPhysica A: Statistical Mechanics and its Applications, 2010
- From dynamical systems to the Langevin equationPhysica A: Statistical Mechanics and its Applications, 1987
- The fluctuation-dissipation theoremReports on Progress in Physics, 1966