## THERMAL SCIENCE

International Scientific Journal

### FRACTIONAL DERIVATIVES OF CONSTANT AND VARIABLE ORDERS APPLIED TO ANOMALOUS RELAXATION MODELS IN HEAT TRANSFER PROBLEMS

**ABSTRACT**

In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.

**KEYWORDS**

PAPER SUBMITTED: 2016-12-16

PAPER REVISED: 2016-12-17

PAPER ACCEPTED: 2016-12-24

PUBLISHED ONLINE: 2017-01-14

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**3**, PAGES [1161 - 1171]

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