Genetic algorithm applied to fractional optimal control of a diabetic patient

Abstract

Diabetes is a dangerous disease that increases in incidence every year. The aim of this paper is to present and analyze the model of diabetes and its complications with the fractional derivative of Caputo, namely, we propose a mathematical model with a fractional derivative of the type 2 diabetes. The positivity and boundedness of the solutions is demonstrated by the Laplace transform method. We study the existence and uniqueness of the solution of the system. We use the genetic algorithm (GA) to solve the fractional differential equation model and to characterize the optimal control and this is an efficient and simple metaheuristic method to implement. Simulations of the total number of diabetics with the different values of a parameter 𝛼 show that the combined control strategy leads to a significant decrease. The simulation results also show that the number of uncomplicated diabetics in the fractional model, for the different fractional values of 𝛼, decreases more rapidly than the integer derivative model.