Inverse Nodal Problem for a Conformable Fractional Diffusion Operator

Trace Formulas for a Conformable Fractional Diffusion Operator

In this paper, the regularized trace formulas for a diffusion operator which include conformable fractional derivatives of order α (0<{α\leq 1}) is obtained.

Inverse problems for a conformable fractional Sturm-Liouville operator

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study on half-inverse problem and prove a Hochstadt and Lieberman-type theorem.

分数p-拉普拉斯在斯特拉赫对称域中的 Payne 节点集猜想

Payne nodal set conjecture for the fractional $p$-Laplacian in Steiner symmetric domains

本文研究了分数p-拉普拉斯在斯特拉赫对称域中特征函数和节点解的边界接触性质，通过极化不等式分析证明了正负部分支持接触边界，并推导出节点集的相同性质。

Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions

We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane and provides a bound on the number of nodal domains for the extensions of the eigenfunctions. Using the combinatorial properties of noncrossing partitions, we turn the nodal domain bound into an estimate for the number of sign changes in the eigenfunctions. We discuss applications in the periodic setting and the Steklov problem on planar domains.