Subdiffusion model with time-dependent diffusion coefficient: Integral-balance solution and analysis

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+β1) 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.