On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise inℝd-Reference-Cited by-同舟云学术

On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise inℝd

Published:2014 Issue: Volume:2014 Page:1-10
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Sun Xichao¹^ORCID,Wang Zhi²,Cui Jing³

Affiliation:

1. Department of Mathematics and Physics, Bengbu College, 1866 Caoshan Road, Bengbu, Anhui 233030, China

2. Department of Mathematics, Donghua University, 2999 North Renmin Road, Songjiang, Shanghai 201620, China

3. Department of Mathematics, Anhui Normal University, 1 East Beijing Road, Wuhu 241000, China

Abstract

We study a stochastic partial differential equation in the whole spacex∈ℝd, with arbitrary dimensiond≥1, driven by fractional noise and a pure jump Lévy space-time white noise. Our equation involves a fractional derivative operator. Under some suitable assumptions, we establish the existence and uniqueness of the global mild solution via fixed point principle.

Funder

Natural Science Foundation of Anhui Province

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/758270.pdf

Reference29 articles.

1. An introduction to stochastic partial differential equations

2. On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension

3. The heat equation with Lévy noise1

4. On a stochastic partial differential equation with a fractional Laplacian operator

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1. Stochastic Fractional Heat Equations Driven by Fractional Noises;MATH PROBL ENG;2015