Hölder continuity of exponential pullback attractors for Form II Mindlin's strain gradient viscoelastic plate

The paper investigates some continuity properties of pullback and exponential pullback attractors of the non-autonomous problem of Form II Mindlin's strain gradient viscoelastic plate derived recently by Aouadi [2]. Under quite general assumptions on nonlinear damping and sources terms, we establish existence and uniqueness of weak and strong solutions. We prove the existence of pullback attractors in the natural space energy, its upper semicontinuity and continuity with respect to the perturbed parameter $ \delta \in (0, 1] $ and its finite fractal dimension. Finally, we prove that the related process has an exponential pullback attractor $ \mathcal{M}_\delta $ for each $ \delta $, and its Hölder continuity on $ \delta\in (0, 1] $. In particular, the continuity on perturbation $ \delta\in (0, 1] $ holds for global and exponential attractors when the non-autonomous dynamical system degenerates to an autonomous one, so the results of the paper deepen and extend those in [2].