Inverse coefficient problems for one-dimensional time-fractional diffusion equations

TL;DR

This paper proves the uniqueness of identifying a spatially varying coefficient in a one-dimensional time-fractional diffusion equation using initial and boundary data, advancing inverse problem theory for fractional PDEs.

Contribution

It establishes the first uniqueness result for inverse coefficient problems in one-dimensional time-fractional diffusion equations with data at a single boundary.

Findings

Uniqueness of the inverse problem is proven under given conditions.

The method applies to fractional diffusion equations with variable coefficients.

Results contribute to the mathematical understanding of inverse problems in fractional PDEs.

Abstract

We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one end point of the spatial interval.