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Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses

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  • Abbas, Saïd
  • Benchohra, Mouffak

Abstract

In this paper, we investigate some uniqueness and Ulam’s type stability concepts of fixed point equations for a class of partial functional differential equations with not instantaneous impulses in Banach spaces. An example is also provided to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:190-198
    DOI: 10.1016/j.amc.2014.06.073
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    Cited by:

    1. Mallika Arjunan, M. & Abdeljawad, Thabet & Kavitha, V. & Yousef, Ali, 2021. "On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    3. Haide Gou & Tianxiang Wang, 2023. "The method of lower and upper solution for Hilfer evolution equations with non-instantaneous impulses," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 499-523, June.
    4. 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.
    5. 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.
    6. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. 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.

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