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Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses

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  • Kumar, Vipin
  • Malik, Muslim
  • Debbouche, Amar

Abstract

In this paper, we prove the existence, stability and controllability results for fractional damped differential system with non-instantaneous impulses. The results are obtained by using Banach fixed-point theorem, nonlinear functional analysis, Mittag-Leffler matrix function and controllability Grammian matrix. At last, some numerical examples are given to illustrate the obtained theory.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320305877
    DOI: 10.1016/j.amc.2020.125633
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    References listed on IDEAS

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    1. Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.
    2. Yang, Dan & Wang, JinRong & O’Regan, D., 2018. "A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 654-671.
    3. Michal Fec̆kan & JinRong Wang & Yong Zhou, 2013. "Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 79-95, January.
    4. JinRong Wang & Michal Fečkan & Amar Debbouche, 2019. "Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 573-587, August.
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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. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Zhu, Zhen & Lu, Jun-Guo, 2021. "Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    4. Vadivoo, B.S. & Jothilakshmi, G. & Almalki, Y. & Debbouche, A. & Lavanya, M., 2022. "Relative controllability analysis of fractional order differential equations with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    5. 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).

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