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A note on the mild solutions of Hilfer impulsive fractional differential equations

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  • Sousa, J. Vanterler da C.
  • Oliveira, D.S.
  • Capelas de Oliveira, E.

Abstract

In this paper, we present a new type of Gronwall inequality and discuss some particular cases. We apply these results to investigate the uniqueness and δ-Ulam–Hyers–Rassias stability of mild solutions of a fractional differential equation with non-instantaneous impulses in a Pδ-normed Banach space. In this sense, we present an example, in order to elucidate one of the results discussed.

Suggested Citation

  • Sousa, J. Vanterler da C. & Oliveira, D.S. & Capelas de Oliveira, E., 2021. "A note on the mild solutions of Hilfer impulsive fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002988
    DOI: 10.1016/j.chaos.2021.110944
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    References listed on IDEAS

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    1. 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.
    2. Jaydev Dabas & Archana Chauhan & Mukesh Kumar, 2011. "Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-20, October.
    3. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
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