Numerical approximation of a time-delayed fractional-order diabetes mellitus model using predictor-corrector method

This paper presents a mathematical model to study diabetes mellitus disease by incorporating fractional derivatives in the Caputo sense, which generalizes classical integer-order models through improved representation of memory effects. The model incorporates fractional time delay and treatment function to enable a more comprehensive analysis of the disease. First, we determine the model's essential equilibria and establish its positivity and boundedness. A qualitative analysis of approximate solutions has been carried out using fixed point theory which is well-suited for handling non-local and nonlinear aspects of fractional order systems. We have performed computational simulations by using an Adams–Bashforth–Moulton-type predictor–corrector approach for different fractional order values. These findings facilitate to advance our understanding of the dynamics of diabetes and can inform the development of effective public health initiatives.