## THERMAL SCIENCE

International Scientific Journal

### MODELLING THE OXYGEN DIFFUSION EQUATION WITHIN THE SCOPE OF FRACTIONAL CALCULUS

**ABSTRACT**

The diffusion of oxygen into human body with simultaneous absorption is an important problem and it is of great importance in medical applications. This problem can be formulated in two stages; At the first stage, the absorption of oxygen at the surface of the medium is constant and an another stage considering the moving boundary problem of oxygen absorbed by the human body. In this paper we obtain analytical solutions for the oxygen diffusion equation considering the Liouville-Caputo, Atangana-Baleanu-Caputo, fractional conformable derivative in the Liouville-Caputo sense and Atangana-Koca-Caputo fractionalorder derivatives. Numerical simulations were obtained for different values of the fractional order.

**KEYWORDS**

PAPER SUBMITTED: 2018-01-08

PAPER REVISED: 2018-08-31

PAPER ACCEPTED: 2018-01-31

PUBLISHED ONLINE: 2018-03-04

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 2**, PAGES [1279 - 1287]

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