In personalized explainable recommendation systems, user ID is an important identifier for personalization. Existing algorithms usually adopt the encoder-decoder architecture to generate personalized explainable recommendations, however, this approach increases the complexity and computational cost of the algorithm and limits the accuracy performance of the algorithm. To address this problem, this study proposes a personalized explainable recommendation algorithm (PERSP) that incorporates self-attention mechanism and prompt learning. The algorithm enhances the interpretability of the algorithm by introducing and fine-tuning prompt learning in the input layer of BERT. To overcome the inability of BERT to directly use user IDs for personalized recommendations, the algorithm uses a self-attentive mechanism to splice user IDs with other commands and feeds the sequences into the input layer of BERT for training and inference. To verify the effectiveness of the algorithm, comparative experiments are conducted on TripAdvisor, Amazon, and Yelp datasets. On the TripAdvisor dataset, the PERSP algorithm improves the root mean squared error (RMSE) and mean absolute error (MAE) by 3.7% and 4.7%, respectively, compared to other baseline algorithms; on the Amazon dataset, the improvements are 1.05% and 4.1% respectively; and on the Yelp dataset, the improvements are 1% and 2.5% respectively. The results show that the algorithm has better performance in personalized explainable recommendation tasks, effectively improving the accuracy and interpretability of recommendation systems.