  This paper is concerned with analysis of coupled fractional
reaction-diffusion equations. It provides analytical comparison for the
fractional and regular reaction-diffusion systems. As an example, the
reaction-diffusion model with cubic nonlinearity and Brusselator model are
considered. The detailed linear stability analysis of the system with Cubic
nonlinearity is provided. It is shown that by combining the fractional
derivatives index with the ratio of characteristic times, it is possible to
find the marginal value of the index where the oscillatory instability arises.
Computer simulation and analytical methods are used to analyze possible
solutions for a linearized system. A computer simulation of the corresponding
nonlinear fractional ordinary differential equations is presented. It is shown
that the increase of the fractional derivative index leads to the periodic
solutions which become stochastic at the index approaching the value of 2. It
is established by computer simulation that there exists a set of stable
spatio-temporal structures of the one-dimensional system under the Neumann and
periodic boundary condition. The characteristic features of these solutions
consist in the transformation of the steady state dissipative structures to
homogeneous oscillations or space temporary structures at a certain value of
fractional index.
