TY - JOUR
TI - Subdiffusion model with time-dependent diffusion coefficient: Integral-balance solution and analysis
AU - Hristov Jordan Y
JN - Thermal Science
PY - 2017
VL - 21
IS - 1
SP - 69
EP - 80
PT - Article
AB - 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.