Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion

In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in usual set-up for dynamical systems generated by differential equations delay terms. This approach different from ones used previous published literature on memory, which carried out Dafermos transformation. As consequence, obtained results provide complete information about attracting sets original problem, instead transformed one. particular, proved also generalize local case.