Abstract Cauchy problems for the generalized fractional calculus
Probability
2021-01-22 v2 Classical Analysis and ODEs
Abstract
We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove a local existence and uniqueness result, then we focus on a generalized Gr\"onwall inequality. Before addressing the inequality, we study some properties of eigenvalues and eigenfunctions of the generalized fractional derivatives. Finally, we prove some consequences of the generalized Gr\"onwall inequality.
Cite
@article{arxiv.2006.09789,
title = {Abstract Cauchy problems for the generalized fractional calculus},
author = {Giacomo Ascione},
journal= {arXiv preprint arXiv:2006.09789},
year = {2021}
}
Comments
22 pages