An Enhanced Collocation Method for Multi-Term Fractional Differential Equations: Development and Application to Disease Dynamics

This paper presents an enhanced collocation-based numerical framework for solving mixed-order fractional differential equations (FDEs) by transforming them into an algebraic system using polynomial expansion and Gauss-Legendre collocation points. The method's high accuracy and robustness are validated through its application to fractional-order models of Monkeypox transmission and Tuberculosis dynamics, achieving perfect agreement with exact solutions and yielding zero error. The results demonstrate that this approach is a powerful and efficient computational tool for handling the memory-dependent characteristics inherent in complex scientific problems, especially in epidemiological modeling.