Stable Distributions and Green’s Functions for Fractional Diffusions

2018 ◽  
Author(s):  
John Nolan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Stable Distributions ◽  
Fractional Diffusions

Stable distributions and green’s functions for fractional diffusions

2019 ◽  
Vol 22 (1) ◽  
pp. 128-138
Author(s):  
John P. Nolan
Keyword(s):  
Green's Functions ◽  
Numerical Solutions ◽  
Green’S Functions ◽  
Stable Distributions ◽  
Heat Equations ◽  
Density Functions ◽  
Fractional Heat Equation ◽  
Weyl Fractional Derivative ◽  
Numerical Representations ◽  
Fractional Diffusions

Abstract Stable distributions are a class of distributions that have important uses in probability theory. They also have a applications in the theory of fractional diffusions: symmetric stable density functions are the Green’s functions of the fractional heat equation. We describe efficient numerical representations for these Green’s functions, enabling their use in numerical solutions of fractional heat equations. We also describe a new connection between stable laws and the Weyl fractional derivative.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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