Abstract Cauchy problems for the generalized fractional calculus

被引：22

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.

引用

页数：22

共 50 条

[31] SINGULAR NONHOMOGENEOUS ABSTRACT CAUCHY AND DIRICHLET TYPE PROBLEMS RELATED BY A GENERALIZED STIELTJES TRANSFORM
BRAGG, LR
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1974, 24 (02) : 183 - 195
[32] SINGULAR NONHOMOGENEOUS ABSTRACT CAUCHY AND DIRICHLET TYPE PROBLEMS RELATED BY A GENERALIZED STIELTJES TRANSFORM
BRAGG, LR
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (02): : A304 - A304
[33] FRACTIONAL CAUCHY PROBLEMS AND APPLICATIONS
Al Horani, Mohammed
Fabrizio, Mauro
Favini, Angelo
Tanabe, Hiroki
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2020, 13 (08): : 2259 - 2270
[34] UNBOUNDED HOLOMORPHIC FUNCTIONAL-CALCULUS AND ABSTRACT CAUCHY-PROBLEMS FOR OPERATORS WITH POLYNOMIALLY BOUNDED RESOLVENTS
DELAUBENFELS, R
JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 114 (02) : 348 - 394
[35] Generalized Fractional Cauchy–Riemann Operator Associated with the Fractional Cauchy–Riemann Operator
Johan Ceballos
Nicolás Coloma
Antonio Di Teodoro
Diego Ochoa–Tocachi
Advances in Applied Clifford Algebras, 2020, 30
[36] THE CAUCHY PROBLEM FOR GENERALIZED ABSTRACT BOUSSINESQ EQUATIONS
Shakhmurov, Veli B.
DYNAMIC SYSTEMS AND APPLICATIONS, 2016, 25 (1-2): : 109 - 122
[37] GENERALIZED SOLUTIONS FOR THE ABSTRACT SINGULAR CAUCHY PROBLEM
Henriquez, Hernan R.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (03) : 955 - 976
[38] ON THE SOLUTIONS TO A GENERALIZED FRACTIONAL CAUCHY PROBLEM
Lupinska, Barbara
Odzijewicz, Tatiana
Schmeidel, Ewa
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2016, 10 (02) : 332 - 344
[39] Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem
Li, Ya-Ning
Sun, Hong-Rui
ABSTRACT AND APPLIED ANALYSIS, 2014,
[40] Application of Functional Calculus to Complex Cauchy Problems
Stéphane Rigat
Computational Methods and Function Theory, 2007, 7 (2) : 509 - 526

← 1 2 3 4 5 →