Abstract Cauchy problems for the generalized fractional calculus. (August 2021)

• Record Type: Journal Article
• Authors: Ascione, Giacomo
• Is Part Of: Nonlinear analysis. Volume 209(2021)
• Publication Date: 2021-08
• Subjects: 34A08 -- 34G20 -- 60K15; Bernstein functions -- Grönwall inequality -- Contraction theorem -- Inverse subordinator; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112339
• Languages: English
• ISSNs: 0362-546X

Abstract

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 Grönwall 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 Grönwall inequality.