Fractal-Fractional Diabetes Mellitus Model Without Genetic Influences: Numerical Investigations

In this study, we present an accurate simulation to examine the behavior of solutions to the mathematical model of diabetes without genetic factors (MMDWGF) in its fractal-fractional form. To accomplish this goal, we provide a potentially approximation method depends Appelltype Changhee polynomials (ACPs). We employ the spectral collocation method (SCM) in accordance with the characteristics of the ACPs. The proposed technique transforms the given model into a non-linear system of algebraic equations. The use of Picard’s theorem to investigate the critical points of the model, the existence of the solution, and originality is given special attention. The outcomes generated by the RK4 method and the ones acquired visually exhibit similarities. We also compared the results of the given method with the numerical scheme that was previously published, where we computed the residual error function with different values of the approximation-order, to estimate the effectiveness and precision of the proposed methodology. Based on our findings, the technique used offers a helpful tool for simulating the solution of these systems. One of the main advantages of the proposed method is that it requires only a few easy steps, does not generate secular boundaries, and does not require a disturbance parameter.