An integrated machine learning and fractional calculus approach to predicting diabetes risk in women

This study presents a novel dual approach for diabetes risk prediction in women, combining machine learning classification with fractional-order physiological modeling. We employ seven machine learning algorithms: Decision Tree, Logistic Regression, Support Vector Machine (SVM), Random Forest, Bagged Trees, Naive Bayes, and XGBoost, to identify key risk factors, with XGBoost demonstrating higher performance. Glucose levels, BMI, blood pressure, and Diabetes Pedigree Function emerged as the most significant predictors across all models. Complementing these data-driven insights, we develop a Caputo fractional-order model that captures the temporal dynamics of glucose-insulin regulation, BMI, and blood pressure. Through fixed-point theorem analysis, we prove the existence and uniqueness of solutions, while numerical implementations using Lagrange polynomial interpolation reveal how varying fractional orders affect metabolic response patterns. This mathematical framework provides unique insights into the progression of diabetes, particularly through its ability to model memory effects and long-term physiological changes. The practical implementation of our research features an intuitive graphical user interface (GUI) that integrates both approaches, enabling real-time risk assessment with dynamic feedback. Our analysis of the Pima Indians dataset confirms important physiological relationships, including age-pregnancy and BMI-skin thickness correlations. This dual-method framework offers clinicians a comprehensive tool for diabetes management, combining the immediate predictive power of machine learning with the longitudinal perspective of fractional-order modeling. The machine learning component provides accurate short-term risk stratification, while the fractional-order model enhances understanding of long-term disease progression. Together, they enable more personalized and proactive care strategies, advancing both the theory and practice of diabetes risk assessment.