APPLICATION OF A FRACTAL FRACTIONAL DERIVATIVE WITH A POWER-LAW KERNEL TO THE GLUCOSE–INSULIN INTERACTION SYSTEM BASED ON NEWTON’S INTERPOLATION POLYNOMIALS

This paper introduces novel numerical schemes based on Newton’s interpolation polynomial for solving a fractal-fractional glucose–insulin regulatory system modeled using the Lotka–Volterra framework. The model incorporates fractal-fractional derivatives with a power-law kernel, extending classical glucose–insulin dynamics. Fixed-point theory establishes solutions’ existence and uniqueness under the Caputo fractal-fractional operator. Hyers–Ulams stability is investigated. By using linear controllers, the Caputo fractal-fractional-order glucose–insulin system can be controlled to equilibrium. This control system has the potential to improve the management of diabetes by providing precise regulation of blood glucose levels. Numerical examples illustrate the effectiveness of the proposed method. To solve the system, the Atangana–Seda numerical scheme, incorporating Newton’s interpolation polynomials, is applied. Simulated results are compared with analytical findings, confirming the accuracy and applicability of the approach to real-world biological systems.