Fractional Sturm-Liouville problem on metric graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Turemuratova, A. A. Kulaev, R. Ch. Sobirov, Z. A. |
| author_facet | Turemuratova, A. A. Kulaev, R. Ch. Sobirov, Z. A. |
| contents | In the present paper, we investigate the fractional analog of the Sturm-Liouville problem on a metric graph using a combination of left Riemann-Liouville and right Caputo fractional derivatives. This combination creates a symmetric and positive analog of the Sturm-Liouville operator. We demonstrated that the operator has a countable number of eigenvalues converging to infinity and analyzed the convergence of the series of the reciprocal eigenvalues, providing estimates for the eigenfunctions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19905 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Sturm-Liouville problem on metric graphs Turemuratova, A. A. Kulaev, R. Ch. Sobirov, Z. A. Analysis of PDEs 34A08, 34B45, 45C05 In the present paper, we investigate the fractional analog of the Sturm-Liouville problem on a metric graph using a combination of left Riemann-Liouville and right Caputo fractional derivatives. This combination creates a symmetric and positive analog of the Sturm-Liouville operator. We demonstrated that the operator has a countable number of eigenvalues converging to infinity and analyzed the convergence of the series of the reciprocal eigenvalues, providing estimates for the eigenfunctions. |
| title | Fractional Sturm-Liouville problem on metric graphs |
| topic | Analysis of PDEs 34A08, 34B45, 45C05 |
| url | https://arxiv.org/abs/2504.19905 |