# Uniqueness of the inverse reaction coefficient problems for nonlocal diffusion models

## TL;DR

This paper proves the uniqueness of inverse reaction coefficient problems for nonlocal diffusion models using nonlocal maximum principles, advancing the understanding of inverse problems in fractional and nonlocal diffusion equations.

## Contribution

It establishes the first uniqueness theorems for IRCPs in nonlocal and multi-term time-fractional diffusion equations based on average flux data.

## Key findings

- Uniqueness of IRCPs for nonlocal diffusion models proven.
- Application of nonlocal maximum principle to inverse problems.
- Results extend to multi-term time-fractional nonlocal diffusion equations.

## Abstract

In this paper, we consider the inverse reaction coefficient problems (IRCPs) for nonlocal diffusion equation and multi-term time-fractional nonlocal diffusion equation from the average nonlocal flux data in external reaction region. Based on the nonlocal maximum principle we established, the uniqueness theorem for IRCPs are proved.