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Ulam–Hyers stability of fractional Langevin equations

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  • Wang, JinRong
  • Li, Xuezhu

Abstract

In this paper, we discuss Ulam–Hyers stability of nonlinear fractional Langevin equations by using the boundedness, monotonicity and nonnegative properties of classical and generalized Mittag-Leffler functions. Further, the same problem for the associated impulsive systems is investigated. Finally, an example is given to illustrate our theoretical results.

Suggested Citation

  • Wang, JinRong & Li, Xuezhu, 2015. "Ulam–Hyers stability of fractional Langevin equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 72-83.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:72-83
    DOI: 10.1016/j.amc.2015.01.111
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    References listed on IDEAS

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    1. Bazzani, Armando & Bassi, Gabriele & Turchetti, Giorgio, 2003. "Diffusion and memory effects for stochastic processes and fractional Langevin equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 530-550.
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    Cited by:

    1. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Zakir Ullah & Amjad Ali & Rahmat Ali Khan & Muhammad Iqbal, 2018. "Existence Results To A Class Of Hybrid Fractional Differential Equations," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 13-17, January.
    3. Kumar, Vipin & Stamov, Gani & Stamova, Ivanka, 2023. "Controllability Results for a Class of Piecewise Nonlinear Impulsive Fractional Dynamic Systems," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    4. Abdulkafi M. Saeed & Mohammed S. Abdo & Mdi Begum Jeelani, 2021. "Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives," Mathematics, MDPI, vol. 9(20), pages 1-17, October.

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