numerical schemes to solve fractional diabetes models

In this article, we propose a new class of nonlinear fractional differential equations of diabetes disease based the concept of Caputo fractional derivative. Two numerical techniques are introduced to analyze the solution the general fractional diabetes model, that describes glucose homeostasis. The first method, which constructed using the nonstandard finite difference technique involves an asymptotically stable difference scheme. This method maintains important properties of the solutions of the studied system, such as the positivity boundedness. The second method is the Jacobi-Gauss-Lobatto spectral collocation approach, known for exponential accuracy. By employing this collocation method, the problem is transformed into a set of algebraic nonlinear equations, simplifying the overall task. Numerical simulations were conducted to compare performance of these two techniques with other standard methods and the analytic solution in specific cases. Our findings show that the Jacobi-Gauss-Lobatto spectral collocation technique provides higher accuracy solving the fractional diabetes model system, while the nonstandard finite difference approach requires lower computational duration.