Fractional diffusion equation and diffusive stresses | Zendy

Povstenko Yuriy | Zendy

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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)

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