Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11851 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914260783726592 |
|---|---|
| author | Dorrego, Gustavo |
| author_facet | Dorrego, Gustavo |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted fractional ultrahyperbolic diffusion on geometrically deformed domains Dorrego, Gustavo Analysis of PDEs 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. |
| title | Weighted fractional ultrahyperbolic diffusion on geometrically deformed domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.11851 |