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.
"Global Solutions for an -Component System of Activator-Inhibitor Type." Abstr. Appl. Anal. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/939405