# Inverse Problems of Determining Sources of the Fractional Partial Differential Equations

## TL;DR

This paper reviews theoretical results on inverse source problems for diffusion equations with Caputo fractional derivatives, focusing on determining unknown source functions in various settings.

## Contribution

It provides a comprehensive survey of inverse source problems for time-fractional diffusion equations, highlighting recent theoretical advances.

## Key findings

- Established uniqueness results for inverse source problems
- Reviewed stability estimates for source identification
- Summarized methods for determining source functions in boundary and interior problems

## Abstract

In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1. determination of time-dependent functions in interior source terms 2. determination of space-dependent functions in interior source terms 3. determination of time-dependent functions appearing in boundary conditions