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<p>In this paper, we formulate a fractional order type 2 diabetes (T2D) model using the Caputo derivative. The model consists of five compartments, each representing a group of susceptible, affected, treated, healthy, and prevented adults. The Gegenbauer wavelet collocation method (GbWCM) and the well-known fractional Euler method (FEM) have been used to evaluate the numerical solutions of the fractional-order T2D model at different values of fractional order and wavelet parameters. In order to solve the fractional order T2D model with GbWCM, we derive the fractional order integral operational matrix for Gegenbauer wavelets using the basic pulse function. Furthermore, several residual error norms and CPU run times are computed and observed separately for each compartment at different values of fractional order and wavelet parameters. The existence and uniqueness of solutions for the fractional-order T2D model are established, along with stability and convergence analysis of the proposed methods. In addition, residual error estimations are illustrated in detail. Numerical simulations demonstrate that the solutions strongly depend on the fractional order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma\)</EquationSource> </InlineEquation>. In general, the proposed fractional order formulation is simpler, more effective, and highly useful for analyzing such epidemic models.</p>

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Stability analysis and numerical simulation of fractional order type-2 diabetes epidemic models using Gegenbauer wavelet collocation method

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Abdullah Abdullah,
  • Mohit Verma

摘要

In this paper, we formulate a fractional order type 2 diabetes (T2D) model using the Caputo derivative. The model consists of five compartments, each representing a group of susceptible, affected, treated, healthy, and prevented adults. The Gegenbauer wavelet collocation method (GbWCM) and the well-known fractional Euler method (FEM) have been used to evaluate the numerical solutions of the fractional-order T2D model at different values of fractional order and wavelet parameters. In order to solve the fractional order T2D model with GbWCM, we derive the fractional order integral operational matrix for Gegenbauer wavelets using the basic pulse function. Furthermore, several residual error norms and CPU run times are computed and observed separately for each compartment at different values of fractional order and wavelet parameters. The existence and uniqueness of solutions for the fractional-order T2D model are established, along with stability and convergence analysis of the proposed methods. In addition, residual error estimations are illustrated in detail. Numerical simulations demonstrate that the solutions strongly depend on the fractional order \(\sigma\) . In general, the proposed fractional order formulation is simpler, more effective, and highly useful for analyzing such epidemic models.