Hybrid machine learning fractional-order framework for mammographic tumor characterization integrating growth dynamics and malignancy prediction

The study develops a new approach that combines machine learning (ML) with fractional-order differential equations (FDE) to study tumor development in mammograms and evaluate cancer risk. XGBoost delivered its peak performance results through a 961-case dataset (46.3% malignant) with 0.832 accuracy and 0.894 AUC scores, while margin features together with patient age served as primary predictive elements. The FDE model showed tumor expansion patterns, which identified two main model-derived transition points at 0.6 cm and 0.8 cm, representing hypothetical risk shifts rather than clinically actionable boundaries, and demonstrated that larger tumors tend to have less complex density and texture patterns. The research used fractional dynamics to resolve clinical paradoxes and applied machine learning techniques for diagnostic uncertainty measurement. The integrated system allows doctors to assess individual risk through the combination of tumor shape data and physical development boundaries, which provides fresh knowledge about tumor progression.