Analysis and application of the fractal-fractional glucose-insulin model via the Atangana-Baleanu derivative

A fractal-fractional-order of a glucose-insulin model with Michaelis-Menten function as a mean rate of insulin degradation, which mimics diabetes pathogenesis, has been proposed in the sense of the Atangana-Baleanu operator. We examine the solution’s existence, uniqueness, and Hyers-Ulam stability based on the fractal-fractional sense. To illustrate its application, a numerical scheme for the fractal-fractional model is applied to a case study. The case study results provide valuable insights into the effectiveness and accuracy of the proposed fractal-fractional glucose-insulin model. They demonstrate how well the model predicts glucose and insulin dynamics in diabetes patients. Furthermore, these results validate the model’s potential for use in clinical settings to improve diabetes management and treatment strategies.