A stochastic noise-driven dynamic model is proposed to study the diffusion of water molecules around a protein surface, under the effect of thermal fluctuations that arise due to the collision of water molecules with the surrounding environment. The underlying dynamics of such a system may be described in the framework of the generalized Langevin equation, where the thermal fluctuations are assumed to be algebraically correlated in time, which governs the non-Markovian behavior of the system. Results of the calculations of mean-square displacement and the velocity autocorrelation function reveal that the hydration water around the protein surface follows subdiffusive dynamics at long times. Analytical expressions for the first passage time distribution, survival probability, mean residence time and mean first passage time of water molecules are derived for different boundary conditions, to analyze hydration water dynamics under the effect of thermally correlated noise. The results depict a unimodal distribution of the first passage time unlike Brownian motion. The survival probability of hydration water follows a stretched exponential decay for both boundary conditions. The mean residence time of the hydration water molecule for different initial positions increases with increase in the complexity/heterogeneity of the surrounding environment for both boundary conditions. The mean first passage time of the water molecule to reach the absorbing/reflecting boundary follows an asymptotic power law with respect to the thickness of the hydration layer, and increases with increase in the complexity/heterogeneity of the environment.