Identifying initial value problem for time‐fractional diffusion equation with Caputo‐like counterpart hyper‐Bessel operator: Optimal error bound analysis and regularization method

2021 ◽  
Author(s):  
Fan Yang ◽  
Qiao‐Xi Sun ◽  
Xiao‐Xiao Li
Keyword(s):  
Diffusion Equation ◽  
Initial Value Problem ◽  
Regularization Method ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Optimal Error ◽  
Time Fractional Diffusion Equation ◽  
Error Bound Analysis ◽  
Optimal Error Bound ◽  
Bound Analysis

A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain

2019 ◽  
Vol 27 (5) ◽  
pp. 609-621 ◽  
Author(s):  
Fan Yang ◽  
Ni Wang ◽  
Xiao-Xiao Li ◽  
Can-Yun Huang
Keyword(s):  
Diffusion Equation ◽  
Regularization Method ◽  
Regularization Parameter ◽  
A Priori ◽  
Symmetric Domain ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spherically Symmetric ◽  
Initial Value ◽  
Time Fractional Diffusion Equation

Abstract In this paper, an inverse problem to identify the initial value for high dimension time fractional diffusion equation on spherically symmetric domain is considered. This problem is ill-posed in the sense of Hadamard, so the quasi-boundary regularization method is proposed to solve the problem. The convergence estimates between the regularization solution and the exact solution are presented under the a priori and a posteriori regularization parameter choice rules. Numerical examples are provided to show the effectiveness and stability of the proposed method.

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