THERMAL SCIENCE

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Ilknur Koca

,

Abdon Atangana

SOLUTIONS OF CATTANEO-HRISTOV MODEL OF ELASTIC HEAT DIFFUSION WITH CAPUTO-FABRIZIO AND ATANGANA-BALEANU FRACTIONAL DERIVATIVES

ABSTRACT
Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.
KEYWORDS
Atangana-Baleanu derivatives, numerical approximation, Cattaneo-Hristov model, elastic media
PAPER SUBMITTED: 2016-02-09
PAPER REVISED: 2016-04-13
PAPER ACCEPTED: 2016-04-20
PUBLISHED ONLINE: 2016-05-08
DOI REFERENCE: https://doi.org/10.2298/TSCI160209103K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 6, PAGES [2299 - 2305]
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Solutions of Cattaneo-Hristov model of elastic heat diffusion with Caputo-Fabrizio and Atangana-Baleanu fractional derivatives

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