Fractional Sturm–Liouville Problem on Metric Graphs
A. A. TuremuratovaNational University of Uzbekistan, 100174, Tashkent, UzbekistanR. Ch. KulaevNorth Ossetian State University after K.L. Khetagurov, Vladikavkaz, RussiaZ. A. SobirovNational University of Uzbekistan, 100174, Tashkent, Uzbekistan
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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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