## THERMAL SCIENCE

International Scientific Journal

### 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**

PAPER SUBMITTED: 2016-01-12

PAPER REVISED: 2016-01-23

PAPER ACCEPTED: 2016-01-24

PUBLISHED ONLINE: 2016-01-30

**THERMAL SCIENCE** YEAR

**2016**, VOLUME

**20**, ISSUE

**Issue 2**, PAGES [757 - 762]

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