This paper investigates a class of neural networks (NNs) with time-varying delays. At first, based on the general exponential function and by using inequality techniques, we establish novel lemmas addressing fixed/preassigned-time synchronization for such NNs. Then, by employing these derived lemmas and designing two effective feedback controllers, we systematically study the fixed-time synchronization (FTS) and preassigned-time synchronization (PRTS) problems of delayed NNs. In addition, the settling-time estimation in our fixed-time stability lemma expresses superior accuracy compared to existing results in previous related works, which can all be viewed as special cases of this paper. Fin... More >