Akademik Veri Yönetim Sistemi
AIMS Mathematics, cilt.11, sa.3, ss.5992-6018, 2026 (SCI-Expanded, Scopus)
This study deals with Caputo–Fabrizio (CF) fractional-order shingles disease model to capture the intrinsic memory and nonlocal properties that govern the progression of herpes zoster within a population. The model is organized into interacting epidemiological compartments and its mathematical soundness is confirmed by establishing both the existence and stability of results through fixed-point theory and fractional theory. To approximate the model behavior, a high accuracy numerical method based on the Lagrangian interpolation technique is constructed, allowing smooth reconstruction of fractional trajectories and robust behavior of nonlocal operators. Complementing this numerical context, an artificial neural network technique is used and trained using the Levenberg–Marquardt optimization algorithm, enabling efficient learning of disease patterns and authentication of numerical fidelity. Performance indicators, involving regression, training test, error histogram, and convergence features, confirm the reliability of the ANN-supported evaluation. The combined modeling, numerical, and computational analysis offers a comprehensive estimation of the fractional dynamics governing shingles transmission, presenting deeper insights into disease evolution and displaying the capacity of fractional operators and intelligent systems to enhance health risk predictive epidemiological modeling.