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Jordan Y. Hristov

TRANSIENT HEAT DIFFUSION WITH A NON-SINGULAR FADING MEMORY: FROM THE CATTANEO CONSTITUTIVE EQUATION WITH JEFFREY’S KERNEL TO THE CAPUTO-FABRIZIO TIME-FRACTIONAL DERIVATIVE

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 background 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: 2016-01-12
PAPER REVISED: 2016-01-23
PAPER ACCEPTED: 2016-01-24
PUBLISHED ONLINE: 2016-01-30
DOI REFERENCE: https://doi.org/10.2298/TSCI160112019H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 2, PAGES [757 - 762]
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Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative

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