The prompt-based approach has demonstrated its success for continual learning problems. However, it still suffers from catastrophic forgetting due to inter-task vector similarity and unfitted new components of previously learned tasks. On the other hand, the language-guided approach falls short of its full potential due to minimum utilized knowledge and participation in the prompt tuning process. To correct this problem, we propose a novel prompt-based structure and algorithm that incorporate 4 key concepts (1) language as input for prompt generation (2) task-wise generators (3) limiting matching descriptors search space via soft task-id prediction (4) generated prompt as auxiliary data. Our experimental analysis shows the superiority of our method to existing SOTAs in CIFAR100, ImageNet-R, and CUB datasets with significant margins i.e. up to 30% final average accuracy, 24% cumulative average accuracy, 8% final forgetting measure, and 7% cumulative forgetting measure. Our historical analysis confirms our method successfully maintains the stability-plasticity trade-off in every task. Our robustness analysis shows the proposed method consistently achieves high performances in various prompt lengths, layer depths, and number of generators per task compared to the SOTAs. We provide a comprehensive theoretical analysis, and complete numerical results in appendix sections. The method code is available in https://github.com/anwarmaxsum/LEAPGEN for further study.