Inverse problems for time-fractional Schr\"odinger equations

TL;DR

This paper investigates inverse problems for time-fractional Schrödinger equations with Caputo derivatives, establishing refined uniqueness results under weaker initial data regularity.

Contribution

It introduces new uniqueness results for inverse problems in fractional Schrödinger equations, reducing regularity assumptions on initial data.

Findings

Refined uniqueness results for inverse problems

Weakening of initial data regularity requirements

Applicability to fractional derivatives with order in (0,1)

Abstract

We study some inverse problems for time-fractional Schr\"odinger equations involving the Caputo derivative of fractional order $\alpha \in (0,1)$. We prove refined uniqueness results from sets of positive Lebesgue measure for various problems by weakening the regularity of initial data.