Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910103047766016 |
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| author | Toshtemirov, Bakhodirjon Mamanazarov, Azizbek |
| author_facet | Toshtemirov, Bakhodirjon Mamanazarov, Azizbek |
| contents | In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation of variables, we establish the existence of eigenvalues and eigenfunctions for the associated spectral problem and prove that the operator possesses a discrete spectrum. Additionally, we establish the relationship between the given data and the unique solvability of the problem, offering new insights into how degeneracy influences fractional diffusion processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients Toshtemirov, Bakhodirjon Mamanazarov, Azizbek Analysis of PDEs Mathematical Physics 35R11, 35K65, In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation of variables, we establish the existence of eigenvalues and eigenfunctions for the associated spectral problem and prove that the operator possesses a discrete spectrum. Additionally, we establish the relationship between the given data and the unique solvability of the problem, offering new insights into how degeneracy influences fractional diffusion processes. |
| title | Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients |
| topic | Analysis of PDEs Mathematical Physics 35R11, 35K65, |
| url | https://arxiv.org/abs/2604.03739 |