## THERMAL SCIENCE

International Scientific Journal

### TRANSIENT HEAT CONDUCTION WITH NON-SINGULAR MEMORY: HEAT FLUX EQUATION WITH A MITTAG-LEFFLER MEMORY NATURALLY LEADS TO ABC DERIVATIVE JORDAN HRISTOV

**ABSTRACT**

A constitutive heat flux equation with a Mittag-Leffler function as a memory kernel is proposed for transient heat conduction. With this new constitutive equation, the energy balance naturally leads to transient heat conduction equation with a damping term represented by the Atangana-Baleanu derivative of Caputo sense.

**KEYWORDS**

PAPER ACCEPTED: 2022-12-19

PUBLISHED ONLINE: 2023-01-07

**THERMAL SCIENCE** YEAR

**2023**, VOLUME

**27**, ISSUE

**Issue 1**, PAGES [433 - 438]

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