THERMAL SCIENCE

International Scientific Journal

Guo-Cheng Wu

,

Dumitru Baleanu

,

Wei-Hua Luo

ANALYSIS OF FRACTIONAL NON-LINEAR DIFFUSION BEHAVIORS BASED ON ADOMIAN POLYNOMIALS

ABSTRACT
A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
KEYWORDS
fractional calculus, two fractional terms, Adomian decomposition method, numerical solutions, Taylor series of fractional order
PAPER SUBMITTED: 2016-04-16
PAPER REVISED: 2016-05-21
PAPER ACCEPTED: 2016-06-15
PUBLISHED ONLINE: 2016-12-03
DOI REFERENCE: https://doi.org/10.2298/TSCI160416301W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE No. 2, PAGES [813 - 817]
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Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

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