Anisotropic solutions of the time-fractional diffusion equation in multiple dimensions

2018/09/29 by Dimiter Prodanov, Prodanov, Dimiter
Mathematics · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1810.00263

Abstract

Anomalous diffusion phenomena are ubiquitous in complex media, such as biological tissues. A wide class of sub-diffusive phenomena phenomena is described by the time-fractional diffusion equation. The paper investigates the case of anisotropic fractional diffusion in the Euclidean space. The solution of the fractional sub-diffusion equation can be expressed in terms of the Wright function and its spatial derivatives, parametrized by the directional unit vector (or alternatively a normal hyperplane). Moreover, the multidimensional case could be expressed as a transformation of the one-dimensional case.

Related

• Solutions of time fractional anomalous diffusion equations with coefficients depending on both time and space variables
• Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems
• Anomalous diffusion for mass transport phenomena I: Analytic solutions to time fractional diffusion
• Numerical simulations of anomalous diffusion
• Fractional diffusion and Lévy stable processes