4.5 Article

Recovering multiple fractional orders in time-fractional diffusion in an unknown medium

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Summary: This paper focuses on a nonlinear inverse problem of recovering the potential function and the fractional orders in a one-dimensional multi-term time-fractional diffusion equation from noisy boundary Cauchy data. The uniqueness of the inverse problem is derived using analytic continuation, Laplace transformation, and Gel'fand-Levitan theory. The Levenberg-Marquardt regularization method with a regularization parameter chosen by a sigmoid-type function is applied to find a stable approximate solution, which is demonstrated through three numerical examples.

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