Abstract
In this paper we are concerned with an inverse problem for determining the order of time fractional derivative in a time fractional diffusion equation (TFDE in short), where the available measurement is given at a single space-time point. The inverse problem is transformed to a nonlinear algebraic equation of the fractional order based on the solution to the forward problem. We prove that the algebraic equation possesses a unique solution by the strict monotonicity of the Mittag-Leffler function, and the inverse problem is of uniqueness. Numerical examples are presented to show the unique solvability of the inverse problem.
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