Background/Objectives: The management of high-risk pregnancies remains a major clinical challenge, particularly regarding the optimal timing of delivery, which has significant implications for both perinatal outcomes and healthcare costs. In this context, computerized cardiotocography (cCTG) offers an objective, non-invasive and cost-effective method for fetal surveillance, providing quantitative measures of heart rate dynamics that reflect autonomic regulation and oxygenation status. This study aimed to develop and validate regression-based machine learning models capable of predicting the duration of neonatal hospitalization—an objective and quantifiable indicator of neonatal well-being—using cCTG parameters obtained outside of labor, binary clinical variables describing the presence or absence of pregnancy pathologies, and gestational age at monitoring and at delivery. Methods: A total of 694 singleton high-risk pregnancies complicated by gestational diabetes, preexisting diabetes, intrahepatic cholestasis of pregnancy, pregnancy-induced or preexisting hypertension, or fetal growth restriction were enrolled. Twenty clinically relevant features derived from cCTG recordings and perinatal data were used to train and evaluate four regression algorithms: Random Forest, CatBoost, XGBoost, and LightGBM against a linear regression model with Ridge regularization serving as a benchmark. Results: Random Forest achieved the highest generalization performance (test R² = 0.8226; RMSE = 3.41 days; MAE = 2.02 days), outperforming CatBoost (R² = 0.7059), XGBoost (R² = 0.6911), LightGBM (R² = 0.6851) and the linear regression benchmark with Ridge regularization (R² = 0.5699) while showing a consistent train–validation–test profile (0.9428 → 0.8042 → 0.8226). The error magnitude (≈2 days on average) is clinically interpretable for neonatal resource planning, supporting the model’s practical utility. These findings justify selecting Random Forest as the final predictor and its integration into a clinician-facing application for real-time length-of-stay estimation. Conclusions: Machine learning models integrating cCTG features with maternal clinical factors can accurately predict neonatal hospitalization duration in pregnancies complicated by maternal or fetal disease. This approach provides a clinically interpretable and non-invasive decision support tool that may enhance delivery planning, optimize neonatal resource allocation, and improve perinatal care outcomes.

We develop a fractional-weighted functional-analytic framework for the analysis of chaotic dynamics in which the governing equations remain classical while the geometry of the underlying Hilbert space is modified. Specifically, we introduce a family of fractional scalar products with singular weights derived from the Riemann–Liouville kernel, generating weighted Hilbert spaces that emphasize late-time dynamics and long-term correlations. Within this framework, the fractional parameter $$\alpha $$ α plays a dual role by controlling temporal localization in the scalar product and acting as an effective probe of dynamical complexity. By embedding trajectories of the classical Lorenz system into these spaces, we show that the value $$\alpha _{\min }$$ α min minimizing the normalized fractional norm exhibits a clear nonlinear correlation with the Kaplan–Yorke dimension $$D_{KY}$$ D KY of the attractor, thereby establishing $$\alpha _{\min }$$ α min as a functional proxy for fractal complexity without modifying the underlying dynamics. To support analysis and computation, we construct orthogonal and complete basis systems adapted to the fractional geometry, including weighted Gram–Schmidt bases and Jacobi polynomial expansions, which enable efficient spectral approximation of chaotic signals and reveal intrinsic temporal asymmetries not captured by standard $$L^2$$ L 2 representations. The proposed approach provides new analytical and spectral tools for detecting bifurcations, quantifying chaotic complexity, and representing fractal structure, offering a complementary alternative to existing methods based on fractional-order dynamical models.