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arXiv · 2504.19905

Fractional Sturm-Liouville problem on metric graphs

A. A. Turemuratova·R. Ch. Kulaev·Z. A. Sobirov
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Abstract

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.

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A. A. Turemuratova, R. Ch. Kulaev, Z. A. Sobirov. 2025-04-28. Fractional Sturm-Liouville problem on metric graphs. https://arxiv.org/abs/2504.19905

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