In this paper, we propose a model that explains the glucose–insulin regulatory system (GIRS). The literature has demonstrated that fractional-order analysis can uncover new aspects of complex systems that were not previously explored. As a result of our studies, the GIRS is stable in its non-linear fractional-order form. Each numerical investigation is derived in order to demonstrate the effectiveness and applicability of fractional order analysis, including the Toufik–Atangana method and the Bernoulli wavelet operational matrix method (BWOMM). An unregulated glucose–insulin system causes a wide variety of biological disorders. These studies may permit a deeper understanding of the regulatory system.