# Carleman estimates for the time-fractional advection-diffusion equations and applications

## TL;DR

This paper develops Carleman estimates for time-fractional advection-diffusion equations, enabling stability analysis of inverse and boundary value problems, thus advancing mathematical tools for fractional PDEs.

## Contribution

It introduces novel Carleman estimates for generalized time-fractional PDEs, facilitating stability results for inverse and Cauchy problems.

## Key findings

- Established Carleman estimates for fractional PDEs
- Proved conditional stability for lateral Cauchy problem
- Analyzed stability of inverse source problem

## Abstract

In this article, we prove Carleman estimates for the generalized time-fractional advection-diffusion equations by considering the fractional derivative as perturbation for the first order time-derivative. As a direct application of the Carleman estimates, we show a conditional stability of a lateral Cauchy problem for the time-fractional advection-diffusion equation, and we also investigate the stability of an inverse source problem.