Modelling the formation of liver zones within the scope of fractional order derivative.

Abdon Atangana,Suares Clovis Oukouomi Noutchie

doi:10.1155/2014/478028

Abdon Atangana, Suares Clovis Oukouomi Noutchie

Open Access

https://doi.org/10.1155/2014/478028

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Abstract

We develop and extend earlier results related to mathematical modelling of the liver formation zone by the adoption of noninteger order derivative. The hidden uncertainties in the model are captured and controlled thanks to the Caputo derivative. The stationary states are investigated and the time-dependent solution is approximated using two recent iteration methods. In particular, we discuss the convergence of these methods by constructing a suitable Hilbert space.

Highlights

One of the most important parts of any animal or human being body is the liver
Since the formation of the liver zone is a very sensitive study issue, it has come to our mind to present the mathematical formula underpinning the formation of the liver zone within the scope of fractional derivative
We achieved this by making use of the wellknown Caputo derivative because it benefits some physical properties that other including but not limited to the RiemanLiouville and the Jumarie fractional derivative

Summary

Introduction

One of the most important parts of any animal or human being body is the liver. The liver is a very important organ of vertebrates and many other flora and fauna [1]. The liver is indispensable for continued existence; there is at this time no way to pay damages for the nonexistence of liver meaning in the long term, even though novel liver dialysis practices can be used in the temporary [1, 2] This gland shows business of a main role in metabolism and has a number of functions in the body, including glycogen storage, decomposition of red blood cells, plasma protein synthesis, hormone production, and detoxification [3]. It is found below the diaphragm in the abdominal-pelvic area of the abdomen. The liver’s extremely dedicated tissues normalize an extensive diversity of highvolume biochemical reactions, including the synthesis and breakdown of small and complex molecules, countless of which are essential for ordinary fundamental functions [3]

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