9 problems

Existence conjecture. Under certain conditions on $W$, there exists a random variable $V$, independent of $W$ and with support in $[0,1]$, such that holds. In terms of…

Let $0<\alpha\leq\frac{1}{2}$ and define … Here $E_{\rho,\beta}$ denotes the Mittag-Leffler function with parameters $\rho$ and $\beta$. Complete-monotonicity conjecture. The funct…

Let $calpha\in(1,2)$, and let $calpsi(t)$ be the function defined in the paper by equation (psidf). Zero-free conjecture. The function $calpsi(t)$ has no zeros on $(0,\infty)$, nam…

Let calpha ainleft(\frac{3}{5}, 1\right). The Mittag-Leffler function $E{\alpha,1}(z)$ is defined by its standard power series, and the imaginary axis is the set…

Smallest-zero conjecture for $E_{\alpha,1}$. For any $\alpha\in(1,2]$, $E_{\alpha,1}(-z^\alpha)>0$ for all $z\in[0,1.559]$. Moreover, as $\alpha\to1+$,

Smallest-zero conjecture for $E_{\alpha,2}$. For each $\alpha\in[\alpha_0,2]$, the equation

Smallest-zero conjecture for $E_{\alpha,\alpha}$. For any $\alpha\in(1,2]$, $E_{\alpha,\alpha}(-z^\alpha)>0$ for all $z\in[0,2.93785]$. Moreover, as $\alpha\to1+$,

Let $n$ and $s$ be the dimension and fractional-order parameters, let $\boldsymbol{x},\boldsymbol{y}$ be points in the underlying Euclidean space, and let $\lambda$ be the temperin…

Volterra–Grunwald–Letnikov equivalence conjecture. Theorem 5, which asserts equivalence of these equations under the stated continuity and zero-initial-condition hypotheses, is val…