A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations

2021 ◽  
Vol 150 ◽  
pp. 111127
Author(s):  
Smina Djennadi ◽  
Nabil Shawagfeh ◽  
Omar Abu Arqub
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Tikhonov Regularization Method ◽  
Fractional Diffusion Equations ◽  
Time Space

Finite element methods for fractional diffusion equations

2020 ◽  
Vol 11 (04) ◽  
pp. 2030001
Author(s):  
Yue Zhao ◽  
Chen Shen ◽  
Min Qu ◽  
Weiping Bu ◽  
Yifa Tang
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Regularity Theory ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
The Past ◽  
Time Space ◽  
Engineering Physics ◽  
Substantial Interest

Due to the successful applications in engineering, physics, biology, finance, etc., there has been substantial interest in fractional diffusion equations over the past few decades, and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast growing. This paper gives a concise overview on finite element methods for these equations, which are divided into time fractional, space fractional and time-space fractional diffusion equations. Besides, we also involve some relevant topics on the regularity theory, the well-posedness, and the fast algorithm.

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