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Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses

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  • Gautam, Ganga Ram
  • Dabas, Jaydev

Abstract

This article contains the existence results of the mild solutions of an abstract semilinear neutral fractional differential equations with not instantaneous impulses. The results are proved by using the theory of analytic α-resolvent family and fixed point theorems. One application involving partial differential equations with impulses are presented.

Suggested Citation

  • Gautam, Ganga Ram & Dabas, Jaydev, 2015. "Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 480-489.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:480-489
    DOI: 10.1016/j.amc.2015.02.069
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    Citations

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    Cited by:

    1. Balasubramaniam, P., 2021. "Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Jayanta Borah & Swaroop Nandan Bora, 2020. "Sufficient Conditions for Existence of Integral Solution for Non-Instantaneous Impulsive Fractional Evolution Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 1065-1082, September.
    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. 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).
    6. 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.

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