Asymptotic Green’s functions for time-fractional diffusion equation and their application for anomalous diffusion problem

2017 ◽  
Vol 475 ◽  
pp. 77-81 ◽  
Author(s):  
Alexey A. Zhokh ◽  
Andrey I. Trypolskyi ◽  
Peter E. Strizhak
Keyword(s):  
Diffusion Equation ◽  
Anomalous Diffusion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Fractional Diffusion Equation ◽  
Time Fractional Diffusion Equation

scholarly journals A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source

2018 ◽  
Vol 20 ◽  
pp. 02007
Author(s):  
Luu Vu Cam Hoan ◽  
Ho Duy Binh ◽  
Tran Bao Ngoc
Keyword(s):  
Diffusion Equation ◽  
Regularization Method ◽  
Fourier Method ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Fractional Diffusion Equation ◽  
Ill Posed ◽  
Inverse Diffusion ◽  
Time Fractional Diffusion Equation

In the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a regularization method to solve it based on the solution given by the Fourier method.

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