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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 807459, 11 pages
http://dx.doi.org/10.1155/2013/807459
Research Article

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

Department of Mathematics, National University of Defense Technology, Changsha 410073, China

Received 27 June 2013; Accepted 18 August 2013

Academic Editor: Agacik Zafer

Copyright © 2013 Tianlong Shen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.