<p>This work proposes a method for modeling and forecasting mortality rates. It provides an improvement over previous studies by incorporating both the historical evolution of the mortality phenomenon and its random behavior. In the first part, we introduce the model and analyze mathematical properties such as the existence of solutions and their asymptotic behavior. In the second part, we apply this model to forecast mortality rates in Spain, showing that it yields better results than classical methods. Life tables play a fundamental role in actuarial and demographic sciences, as they become a basic instrument to analyze survival and death patterns, constructing biometric functions, and assessing longevity-related risks. The model presented here represents a new formulation within the family of non-local diffusion systems used to construct dynamic life tables. By integrating delay terms and stochastic components into a unified framework, it provides a flexible and robust tool capable of capturing both systematic trends and random fluctuations in mortality. This formulation allows the generation of probabilistic trajectories and confidence intervals, which are essential for assessing uncertainty in applications where mortality plays a central role. Because of these features, the model is well suited for actuarial practice, particularly for longevity risk assessment, pricing of life insurance products, and solvency analysis, as well as for demographic applications requiring medium and long term mortality projections.</p>