Haar Wavelet Operational Matrix Approach for the Numerical Solution of Fractional Order Diabetes Mellitus Model (Journal of Nonlinear Modeling and Analysis, 2025)
Diabetes is a chronic disease which many people suffer from seriously. This study introduces a novel approach called the Haar wavelet collocation method (HWCM) to study the analysis and numerical approximation ofthe fractional order diabetes mellitus model. We built the operational matrixof integration (OMI) using the Haar wavelet to solve the diabetes mellitusmodel, a system of fractional differential equations. First, we transform thediabetes mellitus model into a system of algebraic equations using the operational matrix of integration of the Haar wavelet. The obtained system isfurther considered using the Newton-Raphson technique to extract the unknown Haar coefficients. Here, we use the calculus of fractional derivatives ofa mathematical model to study and investigate the dynamic behavior of diabetes. We find numerical results for the validation of fractional order derivatives. Using the model parameter values, these numerical results are seen fromboth mathematical and biological perspectives. Numerical tables and graphical representations provide a visual presentation of the obtained results. Theresults of the developed method, the RK4 method, and the ND solver solutionare compared. The numerical results show how highly accurate and efficientHWCM is in solving the fractional order diabetes mellitus model. Further,we show the method’s efficacy and dynamics in various settings by performingsimulations with parameter values. Mathematica, a mathematical software,has been utilized for numerical computations and implementation.