Soft robotics, with their application in biomedical fields like flexible surgical tools and wearable exo-suits, have revolutionized biomedical practices. To adapt to different scales of application scenarios, our research emphasizes fractal-inspired soft robotics, leveraging the unique scalable and reconfigurable properties of fractal structures. This study focuses on the computational design and simulation of these robots. Traditional modeling methods, apt for rigid robotic arms, falter for soft materials due to their extensive flexibility. We introduced a deep learning strategy with physics-informed neural network for accurate soft robot dynamics modeling. Unlike existing networks optimized for rigid systems, our approach integrates elastic beam theory and deformation laws into Lagrangian Dynamics, making it ideal for simulating fractal soft robotic arms. Compared to conventional finite element simulations and learning approaches, our method shows superior effectiveness. We also conducted simple simulation experiments to show that fractal soft arm is potentially suitable for medical procedures (such as dilating passages) and proved that this fractal-designed soft robotic arm exhibits good portability and adaptability to various scenarios, making it a promising candidate for guiding the design of future surgical robots.