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

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

Chaos, Solitons & Fractals, 2021, vol. 147, issue C

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.

Keywords: Hilfer fractional derivative; Uniqueness; δ-Ulam–Hyers–Rassias stability; Generalized Gronwall inequality; Mild solution; Fractional differential equations (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002988

DOI: 10.1016/j.chaos.2021.110944

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