Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

Abstract

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.

Keywords:

• fractional diffusion equation
• inverse problem
• determination of fractional orders
• eigenfunction expansion
• multi-time-fractional derivatives

AMS Subject Classifications:

• 35R11
• 35R30
• 44A10

Notes

1 Project supported by the Leading Graduate Course for Frontiers of Mathematical Sciences and Physics (The University of Tokyo).