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Jordan Y. Hristov

AN APPROXIMATE SOLUTION TO THE TRANSIENT SPACE-FRACTIONAL DIFFUSION EQUATION: INTEGRAL-BALANCE APPROACH, OPTIMIZATION PROBLEMS AND ANALYZES

ABSTRACT
This paper presents approximate analytical solutions of an initial-boundary value problem of fractional partial differential diffusion equation with spatial Riemann-Liouville fractional derivative. The proposed approximate solutions are based on the concept of a finite penetration depth with the integral-balance method and series expansions of the assumed parabolic profile with undefined exponent. Optimization problems referring to optimal exponents of the assumed parabolic have been developed.
KEYWORDS
approximate analytical solution, integral-balance method, single integration method, double-integration method, spatial-fractional diffusion equation
PAPER SUBMITTED: 2016-01-13
PAPER REVISED: 2016-03-26
PAPER ACCEPTED: 2016-03-28
PUBLISHED ONLINE: 2016-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160113075H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 1, PAGES [309 - 321]
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An approximate solution to the transient space-fractional diffusion equation: Integral-balance approach, optimization problems and analyzes

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