@article{Aleroev2026, 
author = {Temirkhan S. Aleroev and Yulong Li},
title = {A relationship between the algebraic multiplicity of eigenvalues of fractional integral operators and the simplicity of zeros of Mittag–Leffler functions},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {2},
pages = {813-820},
keywords = {algebraic simplicity, fractional Sturm–Liouville, Mittag–Leffler function, simplicity of zeros},
url = {https://www.sciopen.com/article/10.3934/era.2026036},
doi = {10.3934/era.2026036},
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.}
}