Investigation of the stability of the solution of an inverse problem for a half-order fractional diffusion equation

In this thesis, an inverse problem for a fractional diffusion equation is considered. By using the Carleman type inequalities, stability of the solution of the problem is investigated. In this context, the results obtained by Xu et al. (2011) and Yamamoto and Zhang (2012) are discussed. In the first chapter of the thesis, some basic definitions and theorems are given. In the second chapter, two Carleman inequalities for a fractional order diffusion equation and an elliptic operator which were proved by Xu et al. (2011), Eller and Isakov (2000) respectively are examined. In the last chapter, a method for investigating the stability of the solution of the problem which was presented in the paper Yamamoto and Zhang (2012) is analysed.