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.
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页数：22
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共 37 条
  • [11] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2
    CAPUTO, M
    [J]. GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05): : 529 - &
  • [12] Time fractional equations and probabilistic representation
    Chen, Zhen-Qing
    [J]. CHAOS SOLITONS & FRACTALS, 2017, 102 : 168 - 174
  • [13] Solutions of fractional logistic equations by Euler's numbers
    D'Ovidio, Mirko
    Loreti, Paola
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 506 : 1081 - 1092
  • [14] Debnath L., 2003, Int. J. Math. Math. Sci, V2003, P3413, DOI [10.1155/S0161171203301486, DOI 10.1155/S0161171203301486]
  • [15] Debnath L., 2004, Int. J. Math. Educ. Sci. Technol, V35, P487, DOI DOI 10.1080/00207390410001686571
  • [16] Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type
    Diethelm, Kai
    [J]. ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS: AN APPLICATION-ORIENTED EXPOSITION USING DIFFERENTIAL OPERATORS OF CAPUTO TYPE, 2010, 2004 : 3 - +
  • [17] On a class of functional equations
    Fredholm, I
    [J]. ACTA MATHEMATICA, 1903, 27 (01) : 365 - 390
  • [18] Modeling biological systems with an improved fractional Gompertz law
    Frunzo, Luigi
    Garra, Roberto
    Giusti, Andrea
    Luongo, Vincenzo
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 74 : 260 - 267
  • [19] Kilbas A., 2006, THEORY APPL FRACTION
  • [20] Growth Equation of the General Fractional Calculus
    Kochubei, Anatoly N.
    Kondratiev, Yuri
    [J]. MATHEMATICS, 2019, 7 (07)
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