Stochastic classical solutions for space-time fractional evolution equations on a bounded domain

被引：7
|
作者：
Toniazzi, Lorenzo [1 ]
机构：
[1] Univ Warwick, Dept Math, Coventry, W Midlands, England
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 469卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
Inhomogeneous Caputo evolution equation; Restricted fractional Laplacian; Mittag-Leffler functions; Stable Levy processes; Nonlocal boundary condition; DIFFUSION-EQUATIONS; RANDOM-WALKS; CAUCHY-PROBLEMS; SUBORDINATORS; CALCULUS;
D O I：
10.1016/j.jmaa.2018.09.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Space-time fractional evolution equations are a powerful tool to model diffusion displaying space-time heterogeneity. We prove existence, uniqueness and stochastic representation of classical solutions for an extension of Caputo evolution equations featuring time-nonlocal initial conditions. We discuss the interpretation of the new stochastic representation. As part of the proof a new result about inhomogeneous Caputo evolution equations is proven. (C) 2018 Published by Elsevier Inc.
引用
收藏
页码：594 / 622
页数：29
相关论文
共 50 条
  • [1] Singular solutions for space-time fractional equations in a bounded domain
    Chan, Hardy
    Gomez-Castro, David
    Vazquez, Juan Luis
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (04):
  • [2] Space-Time Fractional Stochastic Equations on Regular Bounded Open Domains
    Vo V. Anh
    Nikolai N. Leonenko
    María D. Ruiz-Medina
    [J]. Fractional Calculus and Applied Analysis, 2016, 19 : 1161 - 1199
  • [3] SPACE-TIME FRACTIONAL STOCHASTIC EQUATIONS ON REGULAR BOUNDED OPEN DOMAINS
    Anh, Vo V.
    Leonenko, Nikolai N.
    Ruiz-Medina, Maria D.
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (05) : 1161 - 1199
  • [4] Space-time coupled evolution equations and their stochastic solutions
    Herman, John
    Johnston, Ifan
    Toniazzi, Lorenzo
    [J]. ELECTRONIC JOURNAL OF PROBABILITY, 2020, 25 : 1 - 21
  • [5] On the regularity of weak solutions to space-time fractional stochastic heat equations
    Zou, Guang-an
    Lv, Guangying
    Wu, Jiang-Lun
    [J]. STATISTICS & PROBABILITY LETTERS, 2018, 139 : 84 - 89
  • [6] Stochastic solution of space-time fractional diffusion equations
    Meerschaert, MM
    Benson, DA
    Scheffler, HP
    Baeumer, B
    [J]. PHYSICAL REVIEW E, 2002, 65 (04): : 4
  • [7] Space-time fractional stochastic partial differential equations
    Mijena, Jebessa B.
    Nane, Erkan
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (09) : 3301 - 3326
  • [8] Non-linear Noise Excitation for some Space-Time Fractional Stochastic Equations in Bounded Domains
    Mohammud Foondun
    Jebessa B. Mijena
    Erkan Nane
    [J]. Fractional Calculus and Applied Analysis, 2016, 19 : 1527 - 1553
  • [9] NON-LINEAR NOISE EXCITATION FOR SOME SPACE-TIME FRACTIONAL STOCHASTIC EQUATIONS IN BOUNDED DOMAINS
    Foondun, Mohammud
    Mijena, Jebessa B.
    Nane, Erkan
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (06) : 1527 - 1553
  • [10] Asymptotic properties of some space-time fractional stochastic equations
    Mohammud Foondun
    Erkan Nane
    [J]. Mathematische Zeitschrift, 2017, 287 : 493 - 519
12345