## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 807459, 11 pages.

### Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

Tianlong Shen, Jianhua Huang, and Jin Li

#### Abstract

The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 807459, 11 pages.

**Dates**

First available in Project Euclid: 26 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1393449727

**Digital Object Identifier**

doi:10.1155/2013/807459

**Mathematical Reviews number (MathSciNet)**

MR3121501

**Zentralblatt MATH identifier**

07095375

#### Citation

Shen, Tianlong; Huang, Jianhua; Li, Jin. Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 807459, 11 pages. doi:10.1155/2013/807459. https://projecteuclid.org/euclid.aaa/1393449727