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On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the \(\psi \)-Hilfer operator

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Abstract

We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the \(\psi \)-Hilfer fractional derivative. In addition, we discuss the Ulam–Hyers and Ulam–Hyers–Rassias stabilities of its solutions. A few examples are presented to illustrate the possible applications of our main results.

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Acknowledgements

We are grateful to the anonymous referees for the suggestions that improved the manuscript.

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Authors and Affiliations

  1. Department of Applied Mathematics, Imecc-Unicamp, Campinas, SP, 13083-859, Brazil

    J. Vanterler da C. Sousa & E. Capelas de Oliveira

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  1. J. Vanterler da C. Sousa
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  2. E. Capelas de Oliveira
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Correspondence to J. Vanterler da C. Sousa.

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Sousa, J.V.d.C., de Oliveira, E.C. On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the \(\psi \)-Hilfer operator. J. Fixed Point Theory Appl. 20, 96 (2018). https://doi.org/10.1007/s11784-018-0587-5

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  • DOI: https://doi.org/10.1007/s11784-018-0587-5

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