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Fractional diffusion equation and diffusive stresses
Author(s) -
Povstenko Yuriy
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700134
Subject(s) - fractional calculus , diffusion equation , diffusion , dissipation , diffusion theory , cauchy distribution , order (exchange) , mathematics , mathematical analysis , plane (geometry) , physics , thermodynamics , geometry , engineering , finance , economics , metric (unit) , operations management
A quasi‐static uncoupled theory of diffusive stresses based on the time‐fractional diffusion equation is considered. The Caputo fractional derivative of order α is used. In particular, the proposed theory interpolates the classical theory of diffusive stresses and that without energy dissipation. The fundamental solution to the second Cauchy problem for the fractional diffusion equation in a plane as well as the associated diffusive stresses are obtained in the case α = 3/2. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)