# 变分数阶扩散方程微分阶数的数值反演Numerical Inversion for the Fractional Order in the Variable-Order Time-Fractional Diffusion Equation

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An implicit finite difference scheme is introduced to solve the variable-order time-fractional diffu-sion equation, and an inverse problem of determining the variable fractional order is set forth using the additional measurements at one interior point. The homotopy regularization algorithm is applied to solve the inverse problem, and numerical examples are presented. The computational and inversion results demonstrate that the variable order has important influence on the problem, and that the computations become effective when the variable order goes to 1.

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