In this paper, under some appropriate assumptions, we prove the existence of the minimal pullback \(\cal{D}_{\sigma}^{\cal{H}_{t}}\) -attractors \(\cal{A}_{\cal{D}_{\sigma}^{\cal{H}_{t}}}\) for the non-autonomous nonlocal diffusion equations in the time-dependent space ℌt(Ω). Next, in same phase space, using a priori estimate and energy methods we establish the existence of pullback attractors {Aξ(t)}t∈ℝ and the upper semicontinuity of {Aξ(t)}t∈ℝ and the global attractor A of equation (1.1) with ξ = 0 and ε(t) = 0, that is, \(\lim_{\xi \rightarrow 0^{+}}\ \ \text{dist}_{{\cal{H}}_{t}}(A_{\xi}(t),A)=0.\)
