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STEADY-STATE HEAT CONDUCTION IN A MEDIUM WITH SPATIAL NON-SINGULAR FADING MEMORY: DERIVATION OF CAPUTO-FABRIZIO SPACE-FRACTIONAL DERIVATIVE FROM CATTANEO CONCEPT WITH JEFFREY`S KERNEL AND ANALYTICAL SOLUTIONS

ABSTRACT
Starting from the Cattaneo constitutive relation with a Jeffrey's kernel the derivation of a transient heat diffusion equation with relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been developed. This approach allows seeing the physical back ground of the newly defined Caputo-Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories.
KEYWORDS
PAPER SUBMITTED: 2016-02-29
PAPER REVISED: 2016-05-04
PAPER ACCEPTED: 2016-05-04
PUBLISHED ONLINE: 2016-05-21
DOI REFERENCE: https://doi.org/10.2298/TSCI160229115H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE 2, PAGES [827 - 839]
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© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence