A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator

2017/09/12 by J. Vanterler da C. Sousa, Sousa, J. Vanterler da Costa, E. Capelas de Oliveira +1 · 1 citation
Mathematics · #26A33 #34A12 #34A40 #36A08 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1709.03634

openalex publication_date 2017/09/12 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

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 ψ-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.

Cited by

• Parametric General Fractional Calculus: Nonlocal Operators Acting on Function with Respect to Another Function

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