Global solutions for a strongly coupled fractional reaction-diffusion system in Marcinkiewicz spaces

We prove the existence of solutions to the Cauchy problem for a strongly coupled semilinear reaction-diffusion system in Marcinkiewicz spaces $L^{(p_1,\infty )}\times L^{(p_2,\infty )}$. The exponents $p_1,p_2$ are chosen in a way that allows us to prove the existence of self-similar for this system. We present a fractional version of Yamazaki's inequality, an essential tool that potentially applies to other fractional-in-time PDEs.