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

Hong Wang; Jin Cheng; Xiangcheng Zheng

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

Xiangcheng Zheng, Jin Cheng, Hong Wang

Analysis of PDEs · Submitted 11 Jun 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID1906.04371 (version 1)

Pith ID2EYIC7VT, Pith's permanent record of this paper and its review

CitationHong Wang, Jin Cheng, Xiangcheng Zheng. "Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations." arXiv:1906.04371 (2019). https://pith.science/paper/2EYIC7VT

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension.	contribution 0.63	0.75	0.03	asserted 0.75
s1	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.	result 0.95	0.93	0.95	asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original 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.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites as background 1 paper

In recent years the inverse problems of determining the parameters in (constant-order) tFDEs, in particular the order(s) of tFDEs that was not encountered in the inverse problems of integer-order diffusion equations, have attracted increasingly more research actitivities [ref] .

Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations · Introduction · 0.80

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