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A Gronwall inequality and the Cauchy-type problem by means of $\psi$-Hilfer operator

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arxiv 1709.03634 v1 pith:OBWI25FZ submitted 2017-09-12 math.CA

J. Vanterler da Costa Sousa , E. Capelas de Oliveira This is my paper · ORCID
classification math.CA
keywords cauchy-typegronwallinequalityproblemfractionalgeneralizedhilferanother
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abstract

In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential equation involving the $\psi$-Hilfer fractional derivative and the existence and uniqueness of solutions are discussed. Finally, through generalized Gronwall inequality, we prove the continuous dependence of data on the Cauchy-type problem.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analysis of Impulsive $\varphi$--Hilfer Fractional Differential Equations

    math.DS 2019-08 reject novelty 3.0 of 10

    Extends standard existence, stability, and dependence theorems to impulsive phi-Hilfer fractional differential equations, but the claimed result on dependence on the derivative order is not correctly proved.

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