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A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order

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  • Yang, Dan
  • Wang, JinRong
  • O’Regan, D.

Abstract

In this article, we study asymptotic and smooth properties of solutions to nonlinear non-instantaneous impulsive differential equations involving parameters of integer order and fractional order. We introduce the concept of continuous dependence and differentiability of solutions and establish sufficient conditions to guarantee the solution depends continuously and is differentiable on the initial condition, impulsive parameters and junction parameters. Finally, two models of non-instantaneous impulsive logistic equations are given to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:654-671
    DOI: 10.1016/j.amc.2017.11.025
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    References listed on IDEAS

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    3. 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.
    4. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
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    Cited by:

    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. Li, Qiuyue & Zhou, Yaoming & Cong, Fuzhong & Liu, Hu, 2018. "Positive solutions to superlinear attractive singular impulsive differential equation," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 822-827.
    3. 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.
    4. Meng, Zhijun & Yi, Mingxu & Huang, Jun & Song, Lei, 2018. "Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 454-464.
    5. Liu, Jingna & Qi, Qi & Liu, Bing & Gao, Shujing, 2023. "Pest control switching models with instantaneous and non-instantaneous impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 926-938.
    6. Ren, Jing & Zhai, Chengbo, 2020. "Stability analysis for generalized fractional differential systems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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