Recently, large language models (LLMs) have achieved remarkable breakthroughs, revolutionizing the natural language processing domain and beyond. Due to immense parameter sizes, fine-tuning these models with private data for diverse downstream tasks has become mainstream. Though federated learning (FL) offers a promising solution for fine-tuning LLMs without sharing raw data, substantial computing costs hinder its democratization. Moreover, in real-world scenarios, private client devices often possess heterogeneous computing resources, further complicating LLM fine-tuning. To combat these challenges, we propose HSplitLoRA, a heterogeneous parameter-efficient fine-tuning (PEFT) framework built on split learning (SL) and low-rank adaptation (LoRA) fine-tuning, for efficiently fine-tuning LLMs on heterogeneous client devices. HSplitLoRA first identifies important weights based on their contributions to LLM training. It then dynamically configures the decomposition ranks of LoRA adapters for selected weights and determines the model split point according to varying computing budgets of client devices. Finally, a noise-free adapter aggregation mechanism is devised to support heterogeneous adapter aggregation without introducing noise. Extensive experiments demonstrate that HSplitLoRA outperforms state-of-the-art benchmarks in training accuracy and convergence speed.