Comparison between pre-diabetes and diabetes model in fuzzy and crisp environment: fuzzy differential equation approach

In this paper we propose a mathematical model for diabetes and pre-diabetes in fuzzy environment. Now due to the presence of fuzzy variable, the model is transformed to a fuzzy differential equation. Now we can use the concept of fuzzy differential equation for solving and stable analysis of the model. Here, after comparing the all-kind solutions of fuzzy and crisp solution of diabetes and pre-diabetes model, we can propose a strong point which is biologically meaningful. The conception of strong fuzzy solution and weak solution of fuzzy diabetes and pre-diabetes model are discussed and suggested which is relevant to this model. Stability criteria have been compared in both cases when fuzzy functions are (i)-gH differentiable and when fuzzy functions are (ii)-gH differentiable. In the point of view of biology, our proposed model system provides strong solution as well as acceptable solution when fuzzy functions are (ii)-gH differentiable. The all results are verified graphically and numerically using MATLAB software.