Precision-Oriented Chebyshev Spectral Collocation Framework for Variable-Order Fractional Diffusion Dynamics

This paper presents a novel shifted combined Chebyshev spectral collocation framework for the accurate numerical solution of three classes of variable-order fractional diffusion models. The proposed approach employs two hybrid Chebyshev polynomial representations to construct the approximate solution, providing enhanced flexibility and high spectral accuracy in handling variable-order fractional behavior. Using a collocation scheme, the governing equations together with their initial and boundary conditions are reduced to structured algebraic systems, enabling efficient implementation while maintaining accuracy. Convergence analysis and error estimates are rigorously established and supported by numerical experiments. The results demonstrate high accuracy, fast convergence, and strong computational performance compared to existing methods.