SPACE-TIME FRACTIONAL STOCHASTIC EQUATIONS ON REGULAR BOUNDED OPEN DOMAINS

被引：20

作者：

Anh, Vo V. ^{[1
]}

Leonenko, Nikolai N. ^{[2
]}

Ruiz-Medina, Maria D. ^{[3
]}

机构：

[1] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia

[2] Cardiff Univ, Math Inst, Senghennydd Rd, Cardiff CF24 4AG, S Glam, Wales

[3] Univ Granada, Fac Sci, C Fuente Nueva S-N, E-18071 Granada, Spain

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2016年 / 19卷 / 05期

基金：

澳大利亚研究理事会;

关键词：

Caputo-Djrbashian fractional-in-time derivative; Dirichlet regular bounded open domains; eigenfunction expansion; fractional pseudodifferential elliptic operators; Gaussian spatiotemporal white noise measure; Mittag-Leffler function; Riemannan-Liouville fractional integral and derivative; stochastic boundary value problems; KINETIC-EQUATIONS; RANDOM-FIELDS; DIFFUSION; DRIVEN;

D O I：

10.1515/fca-2016-0061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the definition of a weak-sense Gaussian solution, in the mean-square sense, are derived. The temporal, spatial and spatiotemporal Holder continuity, in the mean-square sense, of the formulated solution is obtained, under suitable conditions, from the asymptotic properties of the Mittag-Leffler function, and the asymptotic order of the eigenvalues of a fractional polynomial of the Dirichlet negative Laplacian operator on such bounded open domains.

引用

页码：1161 / 1199

页数：39

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