In recent years, there has been a considerable increase of interest in the sixth-generation (6G) communications. The advent of 6G wireless communications will facilitate a comprehensive upgrade and transformation of the industry, enabling higher data rates, lower latency, and ubiquitous connectivity. Research on microelectromechanical systems (MEMS) is a crucial element in the advancement of 6G wireless communications. In this paper, we examine the impact of geometric potential on MEMS within the context of fractal space, where a fractal geometric potential MEMS model is proposed and the critical conditions that govern the pull-in phenomenon are elucidated. Moreover, a periodic solution of the model is proposed and compared with other numerical methods.