Dynamics of Fractional Delayed Reaction-Diffusion Equations.

ABSTRACT

The long-term behavior of the weak solution of a fractional delayed reaction-diffusion equation with a generalized Caputo derivative is investigated. By using the classic Galerkin approximation method and comparison principal, the existence and uniqueness of the solution is proved in the sense of weak solution. In addition, the global attracting set of the considered system is obtained, with the help of the Sobolev embedding theorem and Halanay inequality.