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Abstract <p>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.</p>

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Fractional Sturm–Liouville Problem on Metric Graphs

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • A. A. Turemuratova,
  • R. Ch. Kulaev,
  • Z. A. Sobirov

摘要

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.