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arXiv · 2006.09789

Abstract Cauchy problems for the generalized fractional calculus

Giacomo Ascione
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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.

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Giacomo Ascione. 2020-06-17. Abstract Cauchy problems for the generalized fractional calculus. https://arxiv.org/abs/2006.09789

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