Subdiffusion model with time-dependent diffusion coefficient : Integral-balance solution and analysis
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2017-01-01
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Abstract
The paper addresses approximate integral-balance approach to a time-fractional diffusion equation of order 0 < μ < 1 with a time-dependent diffusion coefficient of power-law type D(t) = D0tβ where 0 < β < 1. The form of the solution spreading in a semi-infinite medium through an analysis of the second moment of the approximate solution reveals that depending on the sum μ + β the solution can model subdiffusive (μ + β < 1), superdiffusive (μ + β > 1), or Gaussian (μ + β = 1) process of transport. The optimal exponents of the approximate parabolic profiles have been determined by minimization the mean squared error of approximation over the penetration depth.