Uniqueness in determination of the fractional order in the TFDE using one measurement
arXiv:2111.13017
Abstract
This article deals with an inverse problem of identifying the fractional order in the 1D time fractional diffusion equation (TFDE in short) using the measurement at one space-time point. Based on the expression of the solution to the forward problem, the inverse problem is transformed to a nonlinear algebraic equation. By choosing suitable initial values and the measured point, the nonlinear equation has a unique solution by the monotonicity of the Mittag-Lellfer function. Theoretical testifications are presented to demonstrate the unique solvability of the inverse problem.