In this paper, we focus on human stature, which reflects both genetic inheritance and environmental influences, particularly nutrition. This study introduces a variable-order fractional Caputo model that integrates genetic contributions, nutritional dynamics, and demographic modifiers. By allowing the fractional order α(t) to vary with age, the model captures hereditary memory and delayed responses to environmental changes. Because analytical solutions for such models are rarely feasible, the predictor–corrector scheme was adopted. This method, combining an explicit Adams–Bashforth predictor with an implicit Adams–Moulton corrector, was chosen for its efficiency, stability, and adaptability to variable-order problems. Numerical simulations closely reproduce the WHO Child Growth Standards with minimal error, confirming the reliability of the approach. The study demonstrates that the strength of fractional modeling lies not only in its theoretical framework but also in the numerical method that makes it practical and applicable to pediatric endocrinology, nutrition policy, and family counseling.

The number 12 is a superior highly composite number divisible by 2, 3, 4, and 6. Analyzing natural numbers through their prime factorization reveals striking patterns and symmetries. The duodecimal system, based on 12, provides a natural framework for structuring natural numbers into periods and groups with similar properties. These structures offer an intuitive perspective on the behavior of the divisor and sigma functions and on residue-class constraints relevant to Goldbach-type decompositions. Furthermore, they help to interpret observed patterns in prime gaps, accounting for the prominence of certain gaps and suggesting empirical trends. This article does not claim new theorems in analytic number theory. Its contribution is a unified mod‑12 framework that brings together several classical facts and makes certain structural regularities visually and arithmetically explicit.