Polynomial approximation of Caputo fractional derivatives through the constrained mock-Chebyshev least squares method

In this paper, we present a polynomial interpolation-regression approach for approximating Caputo fractional derivatives from equispaced data. The method relies on the constrained mock-Chebyshev least squares operator to reconstruct the underlying function by means of a global polynomial constructed from uniformly spaced samples. The fractional derivative is then obtained by applying the Caputo operator to the reconstructed polynomial, which leads to weakly singular integrals. Owing to the polynomial structure of the integrand, these integrals can be exactly evaluated by Gauss-Jacobi quadrature rules tailored to the singular kernel. A theoretical error bound for the resulting approximation is established. Numerical experiments confirm the accuracy of the proposed strategy for different fractional orders.