We show how recent existence results for pullback exponential attractors can be applied to non-autonomous delay differential equations with time-varying delays. Moreover, we derive explicit estimates for the fractal dimension of the attractors. As a special case, autonomous delay differential equations are also discussed, where our results improve previously obtained bounds for the fractal dimension of exponential attractors.

We show the existence of an exponential attractor for non-autonomous dynamical system with bounded delay. We considered the case of strong dissipativity then prove that the result remains for the weak dissipativity. We conclude then the existence of the global attractor and ensure the boundedness of its fractal dimension.