scholarly journals Implicit difference approximation for the two-dimensional space-time fractional diffusion equation

2007 ◽  
Vol 25 (1-2) ◽  
pp. 269-282 ◽  
Author(s):  
P. Zhuang ◽  
F. Liu
Keyword(s):  
Diffusion Equation ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Difference Approximation ◽  
Two Dimensional ◽  
Dimensional Space Time ◽  
Time Fractional Diffusion Equation

scholarly journals Subordination Approach to Space-Time Fractional Diffusion

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 415 ◽  
Author(s):  
Emilia Bazhlekova ◽  
Ivan Bazhlekov
Keyword(s):  
Fundamental Solution ◽  
Diffusion Equation ◽  
Numerical Evaluation ◽  
Dimensional Space ◽  
Gaussian Function ◽  
Fractional Diffusion ◽  
Space Time ◽  
Integral Representations ◽  
Dimensional Space Time ◽  
Time Fractional Diffusion Equation

The fundamental solution to the multi-dimensional space-time fractional diffusion equation is studied by applying the subordination principle, which provides a relation to the classical Gaussian function. Integral representations in terms of Mittag-Leffler functions are derived for the fundamental solution and the subordination kernel. The obtained integral representations are used for numerical evaluation of the fundamental solution for different values of the parameters.

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