Repotor:Gongsheng Li

Time: May 28th 2022 9:00am-10:00am

Tencent Meeting:521-256-2412

Title：An inverse fractional order problem in the time fractional diffusion equation by one measurement

Abstract：In this talk, we are concerned with an inverse problem of determining the fractional order in the 1D time fractional diffusion equation 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 analysis on the Mittag-Leffler function, the nonlinear function is differentiable on the fractional order and its derivative takes negative values under suitable limitation for the model parameters, by which the nonlinear equation has a unique solution and the inverse problem is of uniqueness. Theoretical and numerical examples are presented to demonstrate the unique solvability of the inverse problem.