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A problem on the zeros of the Mittag-Leffler function and the spectrum of a fractional-order differential operator. (English) Zbl 1183.34004
Summary: We carry out spectral analysis of one class of integral operators associated with fractional order differential equations that arises in mechanics. We establish a connection between the eigenvalues of these operators and the zeros of Mittag-Leffler type functions. We give sufficient conditions for complete nonselfadjointness and completeness the systems of the eigenvalues.
MSC:
34A08Fractional differential equations
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)