Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates

TL;DR

This paper proves the global Lipschitz stability for determining coefficients in a one-dimensional time-fractional radiative transport equation of half-order, using Carleman estimates to handle the fractional derivative.

Contribution

It introduces a novel application of Carleman estimates to establish stability in a fractional inverse transport problem with half-order derivatives.

Findings

Established global Lipschitz stability for fractional transport coefficients

Developed Carleman estimates for half-order fractional derivatives

Proved uniqueness and stability in a 1D fractional inverse problem

Abstract

We consider a fractional radiative transport equation, where the time derivative is of half order in the Caputo sense. By establishing Carleman estimates, we prove the global Lipschitz stability in determining the coefficients of the one-dimensional time-fractional radiative transport equation of half-order.