Lipschitz stability in inverse source and inverse coefficient problems for a first- and half-order time-fractional diffusion equation

TL;DR

This paper establishes Lipschitz stability estimates for inverse source and coefficient problems in first- and half-order time-fractional diffusion equations using Carleman estimates.

Contribution

It introduces new stability results for inverse problems in fractional diffusion equations, employing Carleman estimates to achieve Lipschitz stability.

Findings

Lipschitz stability estimates are proved for inverse problems.

Carleman estimates are effectively used in fractional diffusion equations.

The results improve understanding of inverse problems in fractional PDEs.

Abstract

We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.