International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 85203, 8 pages
doi:10.1155/IJMMS/2006/85203
Necessary conditions for local and global existence to a
reaction-diffusion system with fractional derivatives
Latp, Centre de Mathématiques et Informatiques, Université de Provence, 39 rue F., Joliot-Curie, 13453 Marseille cedex 13, France
Received 6 August 2006; Revised 21 September 2006; Accepted 10 October 2006
Copyright © 2006 Kamel Haouam and Mourad Sfaxi. 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
We give some necessary conditions for local and global existence of a solution to reaction-diffusion system of type (FDS) with temporal and spacial fractional derivatives. As in the case of single equation of type (STFE) studied by M. Kirane et al. (2005), we prove that these conditions depend on the behavior of initial conditions for large |x|.