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Controllability Results for a Class of Piecewise Nonlinear Impulsive Fractional Dynamic Systems

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  • Kumar, Vipin
  • Stamov, Gani
  • Stamova, Ivanka

Abstract

We study the total controllability for a new class of piecewise nonlinear Langevin fractional dynamic equations with non-instantaneous impulses. New necessary and sufficient conditions are presented for the total controllability of the corresponding linear impulsive systems. Also, the nonlinear case is investigated and controllability criteria are established. We transform the controllability problem into the existence of a fixed point task by defining a nonlinear operator and a proper admissible piecewise control function on a Banach space. Fractional calculus, Mittag-Leffler functions, Gramian type matrices, and the Schauder’s fixed point theorem are employed to develop our main results. Finally, we illustrate the analytical outcome by providing a simulated example.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006981
    DOI: 10.1016/j.amc.2022.127625
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    References listed on IDEAS

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    1. Kumar, Vipin & Malik, Muslim & Debbouche, Amar, 2021. "Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Wang, JinRong & Li, Xuezhu, 2015. "Ulam–Hyers stability of fractional Langevin equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 72-83.
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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).

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