Backward problem for time-space fractional diffusion equations in Hilbert scales

2021 ◽  
Vol 93 ◽  
pp. 253-264
Author(s):  
Dang Duc Trong ◽  
Dinh Nguyen Duy Hai
Keyword(s):  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Backward Problem ◽  
Time Space

On a backward problem for inhomogeneous time-fractional diffusion equations

2019 ◽  
Vol 78 (5) ◽  
pp. 1317-1333 ◽  
Author(s):  
Nguyen Hoang Luc ◽  
Le Nhat Huynh ◽  
Nguyen Huy Tuan ◽  
Le Dinh Long
Keyword(s):  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Backward Problem

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.

Maximum principles for a class of generalized time-fractional diffusion equations

2020 ◽  
Vol 23 (3) ◽  
pp. 822-836
Author(s):  
Shengda Zeng ◽  
Stanisław Migórski ◽  
Van Thien Nguyen ◽  
Yunru Bai
Keyword(s):  
Fractional Derivatives ◽  
Extreme Points ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Maximum Principles ◽  
Variable Order ◽  
Fractional Diffusion Equations ◽  
Caputo Derivatives ◽  
Time Space ◽  
Generalized Time

AbstractTwo significant inequalities for generalized time fractional derivatives at extreme points are obtained. Then, we apply the inequalities to establish the maximum principles for multi-term time-space fractional variable-order operators. Finally, we employ the principles to investigate two kinds of diffusion equations involving generalized time-fractional Caputo derivatives and space-fractional Riesz-Caputo derivatives.

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