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Controllability of Impulsive ψ -Caputo Fractional Evolution Equations with Nonlocal Conditions

Author

Listed:
  • Longfei Lin

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Yansheng Liu

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Daliang Zhao

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

Abstract

This paper is mainly concerned with the exact controllability for a class of impulsive ψ -Caputo fractional evolution equations with nonlocal conditions. First, by generalized Laplace transforms, a mild solution for considered problems is introduced. Next, by the Mönch fixed point theorem, the exact controllability result for the considered systems is obtained under some suitable assumptions. Finally, an example is given to support the validity of the main results.

Suggested Citation

  • Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Controllability of Impulsive ψ -Caputo Fractional Evolution Equations with Nonlocal Conditions," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1358-:d:573599
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    References listed on IDEAS

    as
    1. Xian-Feng Zhou & Song Liu & Wei Jiang, 2013. "Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, July.
    2. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    3. shu, Xiao-Bao & Shi, Yajing, 2016. "A study on the mild solution of impulsive fractional evolution equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 465-476.
    4. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    5. Liang, Jin & Yang, He, 2015. "Controllability of fractional integro-differential evolution equations with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 20-29.
    6. Daliang Zhao & Juan Mao, 2020. "New Controllability Results of Fractional Nonlocal Semilinear Evolution Systems with Finite Delay," Complexity, Hindawi, vol. 2020, pages 1-13, July.
    7. Li, Haitao & Xu, Xiaojing & Ding, Xueying, 2019. "Finite-time stability analysis of stochastic switched boolean networks with impulsive effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 557-565.
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    Cited by:

    1. Mohammed Kbiri Alaoui & Kamsing Nonlaopon & Ahmed M. Zidan & Adnan Khan & Rasool Shah, 2022. "Analytical Investigation of Fractional-Order Cahn–Hilliard and Gardner Equations Using Two Novel Techniques," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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