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Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points

Author

Listed:
  • Yu Chen

    (Department of Mathematics, Guizhou University, Guiyang 550025, China)

  • JinRong Wang

    (Department of Mathematics, Guizhou University, Guiyang 550025, China
    School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

Abstract

This paper gives continuous dependence results for solutions of integer and fractional order, non-instantaneous impulsive differential equations with random impulse and junction points. The notion of the continuous dependence of solutions of these equations on the initial point is introduced. We prove some sufficient conditions that ensure the solutions to perturbed problems have a continuous dependence. Finally, we use numerical examples to demonstrate the obtained theoretical results.

Suggested Citation

  • Yu Chen & JinRong Wang, 2019. "Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points," Mathematics, MDPI, vol. 7(4), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:331-:d:220188
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    References listed on IDEAS

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    1. Abbas, Saïd & Benchohra, Mouffak, 2015. "Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 190-198.
    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. Liu, Shengda & Wang, JinRong & Shen, Dong & O’Regan, Donal, 2019. "Iterative learning control for differential inclusions of parabolic type with noninstantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 48-59.
    4. Zhang, Jun & Wang, JinRong, 2018. "Numerical analysis for Navier–Stokes equations with time fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 481-489.
    5. Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
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