## THERMAL SCIENCE

International Scientific Journal

### SOLUTIONS OF CATTANEO-HRISTOV MODEL OF ELASTIC HEAT DIFFUSION WITH CAPUTO-FABRIZIO AND ATANGANA-BALEANU FRACTIONAL DERIVATIVES

**ABSTRACT**

Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.

**KEYWORDS**

PAPER SUBMITTED: 2016-02-09

PAPER REVISED: 2016-04-13

PAPER ACCEPTED: 2016-04-20

PUBLISHED ONLINE: 2016-05-08

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**6**, PAGES [2299 - 2305]

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