Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus

Tatiana Matseevich and Temirkhan Aleroev ()
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Tatiana Matseevich: Department of Higher Mathematics, National Research Moscow State Civil Engineering University, 26, Yaroslavskoye Shosse, 129337 Moscow, Russia
Temirkhan Aleroev: Department of Higher Mathematics, National Research Moscow State Civil Engineering University, 26, Yaroslavskoye Shosse, 129337 Moscow, Russia

Mathematics, 2023, vol. 11, issue 20, 1-13

Abstract: This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary-value problems for differential equations of fractional order. In particular, we show the positive definiteness of studying operators, which makes it possible to select areas in the complex plane where there are no eigenvalues for these operators.

Keywords: fractional derivative; eigenvalue; eigenfunction; Mittag–Leffler function; spectral analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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