Open AccessSteady-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
Author(s) -
Jordan Hristov
Publication year - 2017
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci160229115h
Subject(s) - fractional calculus , kernel (algebra) , relaxation (psychology) , heat equation , heat kernel , derivative (finance) , space (punctuation) , mathematical analysis , thermal conduction , diffusion , mathematics , constitutive equation , physics , pure mathematics , quantum mechanics , thermodynamics , finite element method , computer science , psychology , social psychology , financial economics , economics , operating system
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