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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 939405, 9 pages
http://dx.doi.org/10.1155/2013/939405
Research Article

Global Solutions for an -Component System of Activator-Inhibitor Type

1Department of Mathematics, College of Sciences, Taibah University, Yanbu, Saudi Arabia
2Department of Mathematics, University of Tebessa, 12002 Tebessa, Algeria
3Department of Mathematics, University of Batna, 05000 Batna, Algeria

Received 15 May 2013; Accepted 17 July 2013

Academic Editor: Khalil Ezzinbi

Copyright © 2013 S. Abdelmalek 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

This paper deals with a reaction-diffusion system with fractional reactions modeling -substances into interaction following activator-inhibitor's scheme. The existence of global solutions is obtained via a judicious Lyapunov functional that generalizes the one introduced by Masuda and Takahashi.