MODIFIED ATANGANA-BALEANU DERIVATIVE IN CAPUTO SENSE FOR DIABETES MODEL: MODELING AND MATHEMATICAL ANALYSIS

Abstract

The metabolic condition known as diabetes mellitus, which is common throughout the world, is characterized by elevated blood glucose levels. These days, fractional calculus is crucial for developing control techniques, understanding the dynamics of insulin and glucose in both normal and diabetic individuals, and solving a number of other real-world issues. This research examines, via a unique approach, the time-fractional Sturis-Tolic model for both normal and type-1 diabetic individuals. Modified fractional differential equations are treated based on the concept of a derivative in the Caputo sense proposed by Atangana-Baleanu. A numerical approximation of this newly updated fractional operator is applied to the Sturis-Tolic model. We offered some key analysis for the Sturis-Tolic model in the presence of this innovative operator. The modified Atangana-Baleanu Caputo derivative model's numerical solution was found using the Laplace Adomian decomposition technique (LADM). At the end, using the suggested scheme for the Sturis-Tolic model, numerical results and simulations are obtained.