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Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel

Author

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  • Jiale Sheng

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Wei Jiang

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Denghao Pang

    (School of Internet, Anhui University, Hefei 230601, China)

  • Sen Wang

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

Abstract

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.

Suggested Citation

  • Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2139-:d:454731
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    References listed on IDEAS

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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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