Fractional Order Modeling and Neural Network Solutions for Diabetes Mellitus: Capturing Complexity and Memory Effects in Population Dynamics

Abstract

Motivation: The present study provides the numerical solutions of the diabetes mellitus model based on its difficulties in a population by executing a robust stochastic neural network structure. The study related to fractional order derivatives is considered more significant as they capture non-local relations and memory effects, which present a precise depiction of complex models with durable anomalous and dependency performances. The mathematical form of the diabetes mellitus model based on its difficulties in a population has a healthy category, susceptible group, classes of diabetics with and without complications, and a category of diabetics with problems experiencing treatment. Method: The numerical solutions of the diabetes mellitus model are presented for three different cases based on the fractional order values using the neural network structure, a log-sigmoid fitness function and twenty numbers of neurons, whereas the dataset is trained by the Levenberg-Marquardt backpropagation. Results: The competency of the proposed neural network solver is perceived by matching the outcomes, absolute error and optimal training. To authenticate the reliability of the solver, several tests like transition state, regression, and error histogram have also been accomplished.

The authors' abstract, as published at the source. Advances in Complex Systems, 2026 · DOI ↗