5 problems

Conjecture for the odd fractional Schrödinger inequality. For every $p\geq 2$,

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…

Local smoothing conjecture. Fix $\alpha\in(0,1)\cup(1,\infty)$. For $p>\frac{2n}{n-1}$, one has