### AIMS Mathematics

2021, Issue 6: 5909-5923. doi: 10.3934/math.2021350
Research article

# Determination of three parameters in a time-space fractional diffusion equation

• Received: 23 November 2020 Accepted: 17 March 2021 Published: 29 March 2021
• MSC : 34A55, 35R30, 65F22, 65L12

• In this paper, we consider a nonlinear inverse problem of recovering two fractional orders and a diffusion coefficient in a one-dimensional time-space fractional diffusion equation. The uniqueness of fractional orders and the diffusion coefficient, characterizing slow diffusion, can be obtained from the accessible boundary data. Two computational methods, Tikhonov method and Levenberg-Marquardt method, are proposed to solving this problem. Finally, an example is presented to illustrate the efficiency of the two numerical algorithm.

Citation: Xiangtuan Xiong, Wanxia Shi, Xuemin Xue. Determination of three parameters in a time-space fractional diffusion equation[J]. AIMS Mathematics, 2021, 6(6): 5909-5923. doi: 10.3934/math.2021350

### Related Papers:

• In this paper, we consider a nonlinear inverse problem of recovering two fractional orders and a diffusion coefficient in a one-dimensional time-space fractional diffusion equation. The uniqueness of fractional orders and the diffusion coefficient, characterizing slow diffusion, can be obtained from the accessible boundary data. Two computational methods, Tikhonov method and Levenberg-Marquardt method, are proposed to solving this problem. Finally, an example is presented to illustrate the efficiency of the two numerical algorithm.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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