A Gronwall inequality and the Cauchy-type problem by means of $\psi$-Hilfer operator
Classical Analysis and ODEs
2017-09-13 v1
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 -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.
Keywords
Cite
@article{arxiv.1709.03634,
title = {A Gronwall inequality and the Cauchy-type problem by means of $\psi$-Hilfer operator},
author = {J. Vanterler da Costa Sousa and E. Capelas de Oliveira},
journal= {arXiv preprint arXiv:1709.03634},
year = {2017}
}
Comments
19 pages