THERMAL SCIENCE

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Jordan Y. Hristov

SUBDIFFUSION MODEL WITH TIME-DEPENDENT DIFFUSION COEFFICIENT: INTEGRAL-BALANCE SOLUTION AND ANALYSIS

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.
KEYWORDS
time-fractional diffusion, integral-balance method, time-dependent diffusivity, approximate solutions
PAPER SUBMITTED: 2016-04-27
PAPER REVISED: 2016-05-30
PAPER ACCEPTED: 2016-06-27
PUBLISHED ONLINE: 2016-10-01
DOI REFERENCE: https://doi.org/10.2298/TSCI160427247H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 1, PAGES [69 - 80]
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Subdiffusion model with time-dependent diffusion coefficient: Integral-balance solution and analysis

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