Uniqueness for inverse problems of determining orders of multi-term   time-fractional derivatives of diffusion equation
  This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof. 
Zhiyuan Li and Masahiro Yamamoto
math.AP