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<p>This paper investigates the simultaneous identification of the space-dependent diffusion coefficient and the fractional orders in the 1D multi-term time-fractional diffusion equation based on boundary measurement data. First, we rigorously establish the uniqueness of the inverse problem by employing analytic continuation, the Laplace transform and the Gel’fand-Levitan theory. The inverse problem is subsequently reformulated as a functional minimization problem using Tikhonov regularization, which is efficiently solved by a trust-region algorithm. Finally, the effectiveness and stability of the proposed method are verified through two numerical examples.</p>

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Simultaneous Inversion for the Space-Dependent Diffusion Coefficient and the Fractional Orders in a Multi-Term Time-Fractional Diffusion Equation

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • X. X. Xiong,
  • Y. S. Li

摘要

This paper investigates the simultaneous identification of the space-dependent diffusion coefficient and the fractional orders in the 1D multi-term time-fractional diffusion equation based on boundary measurement data. First, we rigorously establish the uniqueness of the inverse problem by employing analytic continuation, the Laplace transform and the Gel’fand-Levitan theory. The inverse problem is subsequently reformulated as a functional minimization problem using Tikhonov regularization, which is efficiently solved by a trust-region algorithm. Finally, the effectiveness and stability of the proposed method are verified through two numerical examples.