(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this study, we develop a fractal-fractional pneumonia transmission model using the Atangana-Baleanu derivative to capture long-memory effects. We analyze the existence and uniqueness of the model’s solutions and examine its stability using Hyers-Ulam criteria. Numerical simulations are conducted to explore the influence of different fractional orders on disease dynamics. The results indicate that fractional-order modeling provides a more flexible and accurate framework than classical integer-order models, particularly in representing population heterogeneities and intervention strategies such as vaccination and treatment. This approach enhances our understanding of pneumonia transmission and offers valuable insights for public health decision-making.