Abstract
The existence, uniqueness and Ulam–Hyers type stability for a class of \(\psi \)-Hilfer fractional differential equations will be investigated. To this end, the Banach fixed point principle and a Gronwall inequality involving the \( \psi \)-Riemann–Liouville fractional integral are used. Applications to illustrate the results are given.
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Acknowledgements
J. Vanterler acknowledges the financial support of a PNPD-CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) scholarship of the Postgraduate Program in Applied Mathematics of IMECC-UNICAMP (88882.305834/2018-01). K. B. Lima acknowledges the financial support of a PhD scholarship of the Program in Applied Mathematics of IMECC-UNICAMP (CAPES(001) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico)(160331/2014-5)). We are grateful to the anonymous referees for the suggestions that improved the manuscript.
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Communicated by Vasily E. Tarasov.
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Lima, K.B., Vanterler da C. Sousa, J. & de Oliveira, E.C. Ulam–Hyers type stability for \(\psi \)-Hilfer fractional differential equations with impulses and delay. Comp. Appl. Math. 40, 293 (2021). https://doi.org/10.1007/s40314-021-01686-1
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DOI: https://doi.org/10.1007/s40314-021-01686-1
Keywords
- Delay impulsive differential equation
- \(\psi \)-Hilfer
- Banach fixed-point theorem
- Generalized Gronwall’s inequality
- Stability