A fractional parabolic inverse problem involving a time-dependent magnetic potential

TL;DR

This paper investigates a fractional parabolic inverse problem with a time-dependent magnetic potential, aiming to recover both magnetic and electric potentials from partial exterior measurements of the Dirichlet-to-Neumann map.

Contribution

It introduces a novel approach to simultaneously determine magnetic and electric potentials in fractional parabolic equations using exterior partial data.

Findings

Unique determination of magnetic and electric potentials

Development of a new inverse problem framework for fractional parabolic equations

Potential applications in medical imaging and geophysics

Abstract

We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map.