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.

翻译：本条涉及一个反向问题, 即用一个时点的测量方法来确定 1D 时间分数扩散方程式( 简称TFDE) 的分数顺序。 根据前方问题解决方案的表达方式, 反向问题变成了非线性代数方程。 通过选择合适的初始值和测量点, 非线性方程有一个独特的解决方案, 即 Mittag- Lellfer 函数的单音性。 提出了理论测试, 以证明反向问题的独特性 。