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Mathematical Problems in Engineering
Volume 2016, Article ID 8409839, 7 pages
Research Article

The New Approximate Analytic Solution for Oxygen Diffusion Problem with Time-Fractional Derivative

Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Umuttepe Campus, Izmit, 41380 Kocaeli, Turkey

Received 9 March 2016; Accepted 22 May 2016

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2016 Vildan Gülkaç. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Oxygen diffusion into the cells with simultaneous absorption is an important problem and it is of great importance in medical applications. The problem is mathematically formulated in two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is investigated, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is investigated. In oxygen diffusion problem, a moving boundary is essential feature of the problem. This paper extends a homotopy perturbation method with time-fractional derivatives to obtain solution for oxygen diffusion problem. The method used in dealing with the solution is considered as a power series expansion that rapidly converges to the nonlinear problem. The new approximate analytical process is based on two-iterative levels. The modified method allows approximate solutions in the form of convergent series with simply computable components.