A Problem on the zeros of the Mittag-Leffler function and the spectrum of a fractional-order differential operator
T. S. Aleroev, Moscow Institute of Municipal Services and Construction, Moscow, Russia E. J. Qualitative Theory of Diff. Equ., No. 25. (2009), pp. 1-18.
H. T. Aleroeva, Moscow Technical University of Communications and Informatics, Moscow, Russia
| Communicated by I. Kiguradze. | Received on 2008-01-31 Appeared on 2009-04-27 |
Abstract: 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.
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