Finite dimensionality of global attractors for a non-classical reaction–diffusion equation with memory

In this paper, we consider a periodic boundary value problem for a non-classical reaction–diffusion equation with memory. In other paper, we use the ω -limit compactness of the solution semigroup { S ( t ) } t ≥ 0 to get the existence of a global attractor. The main goal here is to give an estimate of the fractal dimension of the global attractor. By the fractal dimension theorem given by A.O. Celebi et al., we obtain that the fractal dimension of the global attractor for the problem is finite; this makes the results for the non-classical reaction–diffusion equations more substantial and perfect.