Space–time fractional diffusion equations in d-dimensions

2021 ◽  
Vol 62 (8) ◽  
pp. 083304
Author(s):  
E. K. Lenzi ◽  
L. R. Evangelista
Keyword(s):  
Fractional Diffusion ◽  
Space Time ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations

Stochastic solution of space-time fractional diffusion equations

2002 ◽  
Vol 65 (4) ◽  
Author(s):  
Mark M. Meerschaert ◽  
David A. Benson ◽  
Hans-Peter Scheffler ◽  
Boris Baeumer
Keyword(s):  
Fractional Diffusion ◽  
Space Time ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Stochastic Solution

On the invariant solutions of space/time-fractional diffusion equations

2017 ◽  
Vol 91 (12) ◽  
pp. 1571-1579 ◽  
Author(s):  
Fariba Bahrami ◽  
Ramin Najafi ◽  
Mir Sajjad Hashemi
Keyword(s):  
Fractional Diffusion ◽  
Space Time ◽  
Diffusion Equations ◽  
Invariant Solutions ◽  
Fractional Diffusion Equations

Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Małgorzata Klimek ◽  
Agnieszka B. Malinowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Waiting Times ◽  
Liouville Problem ◽  
Fractional Diffusion ◽  
Space Time ◽  
Domain Model ◽  
Diffusion Equations ◽  
Liouville Theory ◽  
Finite Domain ◽  
Fractional Diffusion Equations ◽  
Sturm Liouville

AbstractThe space–time fractional diffusion equations on finite domain model anomalous diffusion behavior with large particle jumps combined with long waiting times. In this work we prove existence of strong solutions for such equations. Our proofs strongly depend on the fractional Sturm–Liouville theory, precisely on the problem of finding eigenvalues and corresponding eigenfunctions to the certain fractional differential equation. Using the method of separating variables and applying theorem ensuring existence of solutions to the fractional Sturm–Liouville problem we solve several types of fractional diffusion equations.

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