This study proposes a novel fractional dynamic modeling framework to investigate the long-term impact of sports participation on human health and lifespan. Using publicly available data from international athletes, we construct a five-dimensional dynamic system that integrates both oscillatory adaptation variables, representing short-term training responses, and cumulative physiological indicators, reflecting long-term health effects. The framework is governed by the three-dimensional Atangana-Baleanu-Caputo (3D-ABC) fractional derivative, which enables a realistic representation of memory effects through its non-singular kernel and adjustable parameters controlling decay and adaptation profiles. Cosine-type memory dynamics are shown to effectively capture the periodic behavior of endurance and training load variables, while stress levels and longevity indices exhibit smooth, long-term accumulation patterns. Model parameters are estimated through data fitting, and sensitivity analysis demonstrates how varying the memory depth and decay rates significantly influence physiological outcomes. Furthermore, a decision-tree-based parameter tuning strategy is developed to guide practical model application. The results highlight the advantages of employing fractional calculus, particularly the 3D-ABC approach, in capturing both rapid and delayed biological adaptation processes. The proposed framework provides a robust theoretical and computational tool for understanding the link between structured physical activity and lifespan extension, while also offering insights for optimizing personalized sports training regimens.
R. A. Ibrahim (Thu,) studied this question.