Abstract
•This paper considers the local asymptotic stability of time-fractional reaction-diffusion systems, which have been shown to provide accurate models of a variety of natural phenomena.•Conditions for the stability of commensurate linear systems are derived by means of the eigenfunction expansion of the Laplacian operator.•We show how incommensurate systems can be transformed into commensurate ones.•We show how nonlinear systems can be linearized by means of their first-order Taylor series approximation.
This paper establishes conditions for the asymptotic stability of time–fractional reaction–diffusion systems. The stability of linear systems is investigated by means of the eigenfunction expansion of the Laplacian operator. Theoretical bounds are placed on the arguments of the infinity of eigenvalues belonging to the instant Jacobian matrix. Nonlinear systems are linearized by means of their Taylor series expansion. Numerical solutions of two realistic examples are presented to illustrate the theoretical findings.