Haar Wavelet Operational Matrix Approach for the Numerical Solution of Fractional Order Diabetes Mellitus Model

Abstract

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 of the fractional order diabetes mellitus model. We built the operational matrix of integration (OMI) using the Haar wavelet to solve the diabetes mellitus model, a system of fractional differential equations. First, we transform the diabetes mellitus model into a system of algebraic equations using the operational matrix of integration of the Haar wavelet. The obtained system is further considered using the Newton-Raphson technique to extract the unknown Haar coefficients. Here, we use the calculus of fractional derivatives of a 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 from both mathematical and biological perspectives. Numerical tables and graphical representations provide a visual presentation of the obtained results. The results of the developed method, the RK4 method, and the ND solver solution are compared. The numerical results show how highly accurate and efficient HWCM is in solving the fractional order diabetes mellitus model. Further, we show the method’s efficacy and dynamics in various settings by performing simulations with parameter values. Mathematica, a mathematical software, has been utilized for numerical computations and implementation.