Abstract Cauchy problems for the generalized fractional calculus

被引：21
作者：
Ascione, Giacomo [1 ]
机构：
[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz Renato Caccioppol, Naples, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 209卷
关键词：
Bernstein functions; Gronwall inequality; Contraction theorem; Inverse subordinator; EQUATIONS; TIMES;
D O I：
10.1016/j.na.2021.112339
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 Gronwall 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 Gronwall inequality. (C) 2021 Elsevier Ltd. All rights reserved.
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页数：22
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