Modelling the impact of education and memory on the management of diabetes mellitus using Atangana-Baleanu-Caputo fractional order model

In this research, the Atangana-Baleanu-Caputo fractional derivative is applied to unravel the effect of memory-dependent behaviors of human awareness to healthy lifestyle and genetic knowledge of diabetes transmission using a mathematical model. By proving the theorems of positivity and invariant regions, the model is ensured to have positive solutions and an invariant domain. Additionally, utilizing Lipschitz and fixed-point theories, the existence of a unique solution for the fractional-order model was guaranteed. The model’s solution, was derived using the Laplace Adomian Decomposition Method, and it is applied to perform numerical experiments. The results, shown in tables and graphs, revealed that promoting awareness of healthy lifestyles and genetic factors, supported by strong retention of information, significantly reduces prediabetes incidence in predisposed individuals.