Global existence of solutions for Gierer-Meinhardt system with three equations

Abstract: This paper deals with an Gierer-Meinhardt model, with three substances, formed Reaction-Diffusion system with fractional reaction. To prove global existence for solutions of this system presents difficulties at the boundednees of fractionar term. The purpose of this paper is to prove the existence of a global solution using a boundary functionel. Our technique is based on the construction of Lyapunov functionel.