Different strategies for diabetes by mathematical modeling: Applications of fractal–fractional derivatives in the sense of Atangana–Baleanu

Abstract

For diabetes mellitus therapies, Bergman’s minimal model is proposed. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the fractal–fractional derivatives in the sense of Atangana–Baleanu. Diabetes mellitus disease dynamics are modeled using this modified derivative. The operator can be applied to formulate memory effects models. We proved the existence and uniqueness of the model solution using fractal–fractional derivatives in the sense of Atangana–Baleanu. The model’s solution and uniqueness, as well as the Hyers-Ulam stability analysis, are established. Moreover, we compare ordinary, Atangana–Baleanu, fractal–fractional derivatives in the sense of Atangana–Baleanu, and the real measured data of 10 subjects. Diabetes mellitus rates increase when both fractal dimensions θ1 and θ2 decrease in numerical experiments. Results from fractal–fractional derivatives in the sense of Atangana–Baleanu are closer to reality than integer-order models.

Keywords

• AB fractal–fractional operator
• Ulam-Hyres stability