Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations

2019/06/11 by Xiangcheng Zheng, Jin Cheng, Hong Wang · 1 citation
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.1088/1361-6420/ab3aa3

arxiv created 2019/06/11 · openalex created_date 2019/06/27 · openalex publication_date 2019/10/24 · arxiv updated 2020/01/08 · openalex updated_date 2026/07/30

Abstract

We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be determined by the behavior of the variable order at the initial time, a uniqueness result for an important inverse problem of determination of the variable order in the time-fractional derivative contained in the proposed model from observations of its solutions is obtained.

Citations

• The random walk's guide to anomalous diffusion: a fractional dynamics approach

Cited by

• Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion

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