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Research Article | Open Access

A relationship between the algebraic multiplicity of eigenvalues of fractional integral operators and the simplicity of zeros of Mittag–Leffler functions

Temirkhan S. Aleroev1, Yulong Li2( )
Department of Applied Mathematics, The National Research Moscow State University of Civil Engineering (NRU MGSU), Yaroslavskoe Highway 26, Moscow 129337, Russia
Department of Mathematics, University of Dayton, 300 College Park Dayton, Dayton, OH 45469, USA
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Abstract

In this short note, we establish a connection between the algebraic multiplicity of eigenvalues of compact integral operators and the simplicity of zeros of a class of the Mittag–Leffler functions E α , α ( z ) and E α , 2 ( z ) for 1 < α < 2. Although these are two seemingly unrelated concepts in mathematics, our approach provides a functional‑analytic criterion for determining the simplicity of zeros in this class of Mittag–Leffler functions.

Keywords

algebraic simplicityfractional Sturm–LiouvilleMittag–Leffler functionsimplicity of zeros

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Electronic Research Archive
Volume 34 Issue 2,
February 2026
Pages 813-820
DOI: 10.3934/era.2026036

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Aleroev TS, Li Y. A relationship between the algebraic multiplicity of eigenvalues of fractional integral operators and the simplicity of zeros of Mittag–Leffler functions. Electronic Research Archive, 2026, 34(2): 813-820. https://doi.org/10.3934/era.2026036

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Received: 30 November 2025
Revised: 31 December 2025
Accepted: 05 January 2026
Published: 23 January 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)