Fractional Sturm–Liouville Problem on Metric Graphs

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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