In many domains, such as healthcare, time-series data is irregularly sampled with varying intervals between observations. This creates challenges for classical time-series models that require equally spaced data. To address this, we propose a novel time-series Transformer called Trajectory Generative Pre-trained Transformer (TrajGPT). It introduces a data-dependent decay mechanism that adaptively forgets irrelevant information based on clinical context. By interpreting TrajGPT as ordinary differential equations (ODEs), our approach captures continuous dynamics from sparse and irregular time-series data. Experimental results show that TrajGPT, with its time-specific inference approach, accurately predicts trajectories without requiring task-specific fine-tuning.