Conditional stability for an inverse source problem for the time-fractional diffusion equation

TL;DR

This paper establishes conditional stability results for identifying an unknown source in a 1D time-fractional diffusion equation using boundary measurements, leveraging Fourier transform and Mittag-Leffler functions.

Contribution

It provides the first proof of conditional stability for this inverse source problem in the context of time-fractional diffusion equations.

Findings

Conditional stability is proven for the inverse source problem.

Fourier transform and Mittag-Leffler functions are key tools.

Results enhance understanding of inverse problems in fractional diffusion.

Abstract

This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier transform and several properties of the Mittag-Leffler functions.