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Jordan Y. Hristov

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
non-linear diffusion, non-singular fading memory, Jeffrey kernel, Caputo-Fabrizio derivative integral balance approach
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 Issue 2, PAGES [827 - 839]
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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

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