Highlights
- A cubic-Hermite product-integration operator is embedded in neural collocation for Caputo time derivatives.
- Weakly singular memory weights are precomputed, so no singular quadrature is performed during training.
- Initial and homogeneous Dirichlet conditions are satisfied exactly by the neural ansatz.
- The Hermite memory approximation strongly outperforms L1 on smooth fractional-derivative benchmarks.
- A reproducible forward test reaches a relative L2 error of 1.98e-5 and the same operator identifies alpha and diffusivity jointly.
