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In this paper, we prove global-in-time existence of strong solutions to aclass of fractional parabolic reaction-diffusion systems posed in a boundeddomain of $\mathbb{R}^N$. The nonlinear reactive terms are assumed to satisfynatural structure conditions which provide non-negativity of the solutions anduniform control of the total mass. The diffusion operators are of type$u_i\mapsto d_i(-\Delta)^s u_i$ where $0<s<1$. Global existence of strongsolutions is proved under the assumption that the nonlinearities are at most ofpolynomial growth. Our results extend previous results obtained when thediffusion operators are of type $u_i\mapsto -d_i\Delta u_i$. On the other hand,we use numerical simulations to examine the global existence of solutions tosystems with exponentially growing right-hand sides, which remains so far anopen theoretical question even in the case $s=1$.

A class of fractional parabolic reaction-diffusion systems with control of total mass: theory and numerics