Fractional Sturm-Liouville problem on metric graphs
Analysis of PDEs
2025-04-29 v1
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.
Cite
@article{arxiv.2504.19905,
title = {Fractional Sturm-Liouville problem on metric graphs},
author = {A. A. Turemuratova and R. Ch. Kulaev and Z. A. Sobirov},
journal= {arXiv preprint arXiv:2504.19905},
year = {2025}
}
Comments
Submitted to "Lobachevskii Journal of Mathematics"