Mittag-Leffler functions and convex ordering
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909943674699776 |
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| author | Ferreira, Rui Simon, Thomas |
| author_facet | Ferreira, Rui Simon, Thomas |
| contents | The monotonicity of the Mittag-Leffler function $E_α$ with respect to the parameter $α$ is investigated, via some convex ordering properties for related random variables. In particular, it is shown that the mapping $α\mapsto E_α(x^α)$ decreases on $(0,2)$ for all $x> 0$, that the mapping $α\mapsto E_α(-x^α)$ decreases on $(0,1)$ for all $x\ge 1$ and that the mapping $α\mapsto E_α(Γ(1+α)x)$ decreases on $(0,1)$ for all $x\in{\mathbb R}^\ast.$ Analogous results are presented for the two parameter Mittag-Leffler functions $E_{α, β}$ with $β\ge α,$ with an emphasis on the extremal case $β=α.$ Several applications of these results are discussed for Abelian integral equations and subdiffusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mittag-Leffler functions and convex ordering Ferreira, Rui Simon, Thomas Classical Analysis and ODEs Probability The monotonicity of the Mittag-Leffler function $E_α$ with respect to the parameter $α$ is investigated, via some convex ordering properties for related random variables. In particular, it is shown that the mapping $α\mapsto E_α(x^α)$ decreases on $(0,2)$ for all $x> 0$, that the mapping $α\mapsto E_α(-x^α)$ decreases on $(0,1)$ for all $x\ge 1$ and that the mapping $α\mapsto E_α(Γ(1+α)x)$ decreases on $(0,1)$ for all $x\in{\mathbb R}^\ast.$ Analogous results are presented for the two parameter Mittag-Leffler functions $E_{α, β}$ with $β\ge α,$ with an emphasis on the extremal case $β=α.$ Several applications of these results are discussed for Abelian integral equations and subdiffusions. |
| title | Mittag-Leffler functions and convex ordering |
| topic | Classical Analysis and ODEs Probability |
| url | https://arxiv.org/abs/2512.04940 |