This work introduces the Capacitated Mobile p-Median Problem with Dynamic Demand (CMpMP-DD), an extension of the classical Capacitated p-Median Problem that considers mobile facilities serving time varying customer demands while respecting capacity and movement constraints. We present a Mixed Integer Linear Programming formulation that determines initial facility placement, movement trajectories, and customer assignments over a discrete time horizon. Computational experiments based on real world data from the Provence-Alpes-Côte d'Azur (PACA) region illustrate the model's potential for optimizing mobile service delivery in regional planning contexts.