Uniqueness in inverse boundary value problems for fractional diffusion equations

TL;DR

This paper addresses an inverse boundary value problem for fractional diffusion equations with multiple derivatives, establishing uniqueness in identifying the number, orders, and spatially varying coefficients of the derivatives.

Contribution

It proves the first uniqueness result for determining multiple fractional derivative orders and coefficients in such diffusion equations.

Findings

Uniqueness in identifying the number of fractional derivatives

Uniqueness in determining the orders of derivatives

Uniqueness in recovering spatially varying coefficients

Abstract

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and spatially varying coefficients.