Dynamic networks are widely utilized in social media, biological networks, and various other fields. Accurate prediction of their link evolution is crucial for understanding dynamic behaviors. However, existing methods still face several challenges in link prediction. First, effectively capturing long-term dependencies in time-series modeling remains difficult, and existing approaches struggle to adapt to irregular time intervals. Second, the ability to extract frequency characteristics in non-stationary signals is limited, making it difficult to capture local abrupt changes and periodic patterns in dynamic networks. To address these issues, we proposes the Frequency-Aware Transformer for Dynamic Graphs (FATDyG) framework. Specifically, a time-difference-aware GRU is employed to capture short-term dependencies while adapting to irregular time intervals. Meanwhile, long-term dynamic relationships are modeled using the global attention mechanism of the Transformer. Additionally, discrete cosine transform (DCT) is leveraged to extract periodic features in the frequency domain, and dynamic frequency selection is introduced to enhance the fusion of long- and short-term features. Experiments on seven real-world dynamic network datasets demonstrate that FATDyG outperforms existing methods in link prediction tasks. Compared to baseline approaches, FATDyG achieves up to 3.52% and 1.22% improvements in Average Precision (AP) and the Area Under the Receiver Operating Characteristic Curve (AUC-ROC) respectively, validating its effectiveness.