H\"older stability estimate in an inverse source problem for a first and half order time fractional diffusion equation

TL;DR

This paper establishes a H"older stability estimate for an inverse source problem in a first and half order time fractional diffusion equation, using Carleman estimates and the Bukhgeim-Klibanov method.

Contribution

It introduces a novel Carleman estimate for the fractional diffusion equation and applies it to prove stability in the inverse source problem.

Findings

H"older stability estimate established for the inverse problem

Carleman estimate derived for fractional diffusion equations

Method demonstrates stability with data at a fixed time

Abstract

We consider the first and half order time fractional equation with the zero initial condition. We investigate an inverse source problem of determining the time-independent source factor by the data at an arbitrarily fixed time and we establish the conditional stability estimate of H\"older type in our inverse problem. Our method is based on the Bukhgeim-Klibanov method by means of the Carleman estimate. We also derive the Carleman estimate for the first and half order time fractional diffusion equation.