Optimization with respect to order in a fractional diffusion model:   analysis, approximation and algorithmic aspects
  We consider an identification problem, where the state $u$ is governed by a fractional elliptic equation and the unknown variable corresponds to the order $s \in (0,1)$ of the underlying operator. We study the existence of an optimal pair $(\bar s, \bar u)$ and provide sufficient conditions for its local uniqueness. We develop semi-discrete and fully discrete algorithms to approximate the solutions to our identification problem and provide a convergence analysis. We present numerical illustrations that confirm and extend our theory. 
Harbir Antil and Enrique Otarola and Abner J. Salgado
math.NA