5 problems

Let $E(t)$ denote the beam's energy, let $\alpha$ be the fractional derivative order, and let $\eta$ be the associated parameter. Conjecture. For $\alpha=0.5$ (or similar values) a…

Let $A:\mathbb{R}^d\to\mathbb{R}^{d\times d}$ be a bounded, measurable and strictly elliptic matrix such that … for some $a_*,a^*>0$, for every $x\in\mathbb{R}^d$ and all…

Extension conjecture. The method used to prove the displayed inequalities should also yield analogous inequalities for other fractional derivatives.

Restriction conjecture. The restrictions imposed on $p$ and $\alpha$ in the theorem cannot be removed.

The Grünwald-Letnikov fractional derivative of a function $f$ and the Riemann-Liouville fractional derivative are defined, respectively, by the classical Grünwald-Letnikov limit an…