As the geological exploration data is relatively sparse, unevenly distributed, and contains many geological faults, simple geological surface reconstruction has certain limitations. Based on the fractional differential equations, the paper establishes a subsidence prediction model in exploring geological and mineral resources. The dynamic system described by the reaction-diffusion equation can be mapped to a nonlinear cellular network through space and time discretization. At the same time, the original partial differential equations can be transformed into ordinary differential equations. Furthermore, we can use the difference method to simulate its evolutionary behavior quantitatively. The research results show that the error accuracy between the prediction results of the fractional gray theory established in this paper and the actual engineering results is higher.