An investigation of global existence of the solution of fractional reaction-diffusion system

This paper investigates the existence of the solution for one of the most important fractional partial differential problems called fractional reaction-diffusion system. In particular, with the use of combining the compact semigroup methods and some L¹-estimates, we prove the global existence of the solution for the fractional reaction-diffusion system. Our investigation can be applied to a wide class of fractional partial differential equations even if they contain nonlinear terms in their constructions.