Mathematical analysis and optimal control of a Caputo fractional diabetes system with parameter identification

Abstract

In this study, mathematical modeling of diabetes disease is handled with the Caputo fractional derivative, and the resulting fractional differential equation system is examined in detail. The existence of the solution of this system was mathematically proven under appropriate conditions. Then, for the management and treatment of diabetes, three control parameters are added, and the number of people with diabetes is tried to be kept in the desired range with the optimal control theory. In addition to this, our model gains from parameter estimation and fitting with more accurately generated parameters. The numerical results of the fractional model and the effect of the control parameters are determined with the optimal control approach on glucose levels, examined with various simulations, and presented graphically.