Mathematical modeling of fractional reaction-diffusion systems with different order time derivatives. (English) Zbl 1199.35152

Mat. Metody Fiz.-Mekh. Polya 51, No. 3, 193-201 (2008) and J. Math. Sci., New York 165, No. 3, 392-402 (2010).
Stability analysis is carried out for a two-component fractional reaction-diffusion system with different indices of derivatives for each equation. Two different cases are considered: when the derivative of the activator equation is larger than that of the inhibitor equation and vice versa when the order of the derivative of the equation with positive feedback is less than that of the equation with negative feedback. The general analysis is confirmed by computer simulation of a system with cubic nonlinearity.


35K57 Reaction-diffusion equations
26A33 Fractional derivatives and integrals