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Diffusion problems in fractal media defined on Cantor sets. (English) Zbl 1187.80011

Summary: 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.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
28A80 Fractals
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