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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11851 |
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Table of Contents:
- Standard fractional models on manifolds often conflate geometric anisotropy with medium heterogeneity. In this Letter, we overcome this rigidity by deriving the fundamental solution for a weighted space-time fractional ultrahyperbolic operator, denoted by $(-\Box_{ϕ,ω})^β$. Using a novel spectral approach based on the Weighted Fourier Transform, we explicitly \textbf{decouple the medium density from the geometric deformation}. A crucial finding is the emergence of a \textbf{geometry-independent drift mechanism} driven purely by the inhomogeneity of the medium. The Green's function is obtained in closed form via the Fox H-function, providing a unified and computable framework for anomalous transport in complex, structurally deformed media.