This paper presents a novel mathematical model for diabetes transmission and progression, called SDC, which captures the dynamics of susceptible, uncomplicated, and complicated diabetes cases. Further, the study proposes a fractional-order technique for the diabetes epidemic model to observe the dynamics of disease in society with complications and non-complications. We treated positiveness, boundedness of solutions, and positively invariant regions for this. Through the fixed-point theory, the effect of global derivatives is explored. Also, the uniqueness and existence of solutions are verified. The stability analysis of the model employing the Lyapunov method approach applicable for first and second-order derivative tests is carried out, revealing how the collapse of equilibrium points is influenced by the propagation rate in the disease dynamics. Sensitivity analysis is used to identify the key parameters that drive the propagation rate. For the proposed study using a two-step Lagrange polynomial, we construct the comparative results with a generalized version of the Mittag-Leffler kernel through simulation of various orders of fractional derivative for \(\alpha \) . Through numerical simulations, the theoretical findings are illustrated, highlighting the potential of the SDC model for informing effective diabetes management strategies. Overall, this study contributes to the development of the field of controlling diabetes transmission and providing control measures for its progression.