A relationship between the algebraic multiplicity of eigenvalues of fractional integral operators and the simplicity of zeros of Mittag–Leffler functions
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_{\alpha, \alpha}(z) $ and $ E_{\alpha, 2}(z) $ for $ 1 < \alpha < 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.
Fields of Study & Subjects
Mathematical functions and polynomials
Spectral Theory in Mathematical Physics
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Electronic Research Archive
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 34
- Issue
- 2
- Pages
- 813–820
- Publication date
- 1 January 2026