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The work presents an integral solution of the time-fractional subdiffusion equation as alternative approach to those employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer) well known from the heat diffusion and hydrodynamics. The profile satisfies the boundary conditions imposed at the boundary of the boundary layer that allows its coefficients to be expressed through the boundary layer depth as unique parameter describing the profile. The technique is demonstrated by a solution of a time fractional radial equation concerning anomalous diffusion from a central point source in a sphere.
PAPER REVISED: 2010-10-15
PAPER ACCEPTED: 2010-11-11
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THERMAL SCIENCE YEAR 2011, VOLUME 15, ISSUE Supplement 1, PAGES [S5 - S20]
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