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Diffusion problems in fractal media defined on Cantor sets
Author(s) -
Carpinteri A.,
Sapora A.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900376
Subject(s) - fractal , diffusion , thermal conduction , transient (computer programming) , mathematics , steady state (chemistry) , statistical physics , fractional calculus , anomalous diffusion , simple (philosophy) , mathematical analysis , calculus (dental) , physics , computer science , innovation diffusion , thermodynamics , philosophy , operating system , medicine , knowledge management , chemistry , dentistry , epistemology
In this paper, a fractional approach to describe the diffusion process in fractal media is put forward. After introducing anomalous diffusion quantities, the continuity and constitutive equations are derived by means of local fractional calculus, and the problem is formulated both in the steady‐state regime and in the transient regime. Eventually, a simple heat conduction problem in the steady‐state regime is solved analytically.