A $ (Q,\tau)$ -FRACTIONAL AGING MODEL WITH MEMORY EFFECTS AND ADAPTIVE HEALING DYNAMICS

We propose a novel $(q, \tau)$-fractional aging model that incorporates memory-dependent physiological decay and healing dynamics through a deformable time structure. The model generalizes classical aging laws by introducing a tunable fractional order $ \alpha $ and deformation parameters $ q $ and $ \tau $, which control the depth and scale of biological memory. External interventions, modeled as healing inputs, are integrated via generalized Mittag-Leffler kernels to capture both cumulative and periodic therapeutic effects. Simulation results demonstrate that composite healing strategies significantly delay decline and improve physiological resilience. Parameter sensitivity analysis reveals that the model flexibly adapts to different aging profiles by adjusting memory and deformation parameters. Using synthetic data, we validate the model's fitting accuracy through numerical optimization, achieving high fidelity with low residual error. The key advantage of the $(q, \tau)$-fractional approach lies in its ability to encode long-term memory effects and nonuniform biological time flow, enabling realistic modeling of aging phenomena beyond exponential decay. The framework is robust under noisy conditions and extensible to data-driven calibration, making it a powerful tool for biomedical aging analysis, intervention design, and longitudinal health forecasting.