The Lane–Emden equation (LEE) is essential for modeling the structure of self-gravitating, spherically symmetric polytropic stars in hydrostatic equilibrium. Astronomy commonly employs it to depict normal stars, white dwarfs, and other celestial systems. This paper presents a new formulation of the LEE using truncated M-fractional derivatives (TMD), providing a fractional generalization that expands the conventional comprehension of polytropic gas spheres. Using the accelerated power series approach, we find solutions to the TMD Lane–Emden equation and create polytropic models spanning a variety of polytropic indices. Our results give fundamental insights into stellar properties: whereas the initial zero of the fractional Lane–Emden function grows with decreasing fractional parameters, the radius and mass of polytropic models representing stars like the Sun and white dwarfs decrease under the same circumstances. This mismatch underlines the importance of fractional factors on the structural scaling of stars, offering a broader insight into their physical features. The fractional polytropic models presented here expand the classic theory of polytropes and provide possible applications in comprehending the complex behavior of varied astrophysical phenomena under fractional calculus frameworks.

Under-five mortality remains a significant public health challenge in the Central African Republic (CAR), yet research on the region-specific determinants of this issue is limited. This study explores the use of machine learning (ML) models to predict under-five mortality in CAR using data from the 2018–2019 Multiple Indicator Cluster Survey (MICS). Advanced ML models, including CatBoost (CATB), Light Gradient Boosting (LGB), Extreme Gradient Boosting (XGBoost), and Extreme Gradient Boosting Random Forest (XGBRF), were compared with traditional logistic regression, with model performance evaluated using accuracy metrics such as the Area Under the Curve (AUC), F1 score, Precision, Recall, and Matthews Correlation Coefficient (MCC). CATB outperformed all models, achieving an AUC of 0.973, accuracy of 0.946, F1 score of 0.951, and MCC of 0.897, demonstrating its robust predictive power. The study identified key factors influencing under-five mortality in CAR, such as birth type, maternal education, birth order, birth interval, and birth weight. It suggests that using advanced ML models, particularly CATBoost, can improve identifying region-specific risk factors and inform targeted interventions to reduce child mortality in CAR.