Radius Model for Some Cells in Human Body on Multiplicative Calculus

Abstract

The cell is the basic structure and process unit that carries all the living characteristics of a living thing and has the ability to survive on its own under suitable conditions. The relationship of cell size with nutrient absorption and nutrient consumption in the cell membrane has been examined with the current model using the theory of differential equations in classical analysis. During these examinations, the cell considered was assumed to be spherical. In fact, the shapes of cells vary depending on their functional properties. Many have long appendages, cylindrical parts or branch-like structures. However, in this study, a simple global cell will be discussed, leaving all these complex situations aside. In the current model, the relationship between the change in the radius of the cell and the nutrient absorption and consumption in the cell membrane is detailed using classical differential equations. The answer to the question for which cell size is the consumption rate exactly balanced with the absorption rate was found in classical analysis. The current model consists of first-order differential equations. In this model, the dependent variables are the radius of the cell and the mass of the cell. The classical solutions of these models will be examined, the size of the cell and the cell membrane relationship will be examined, and details will be given with numerical examples. However, in order to consider this biological phenomenon from different perspectives and compare the results, the relevant event will be modeled using multiplicative analysis, one of the Non-Newtonian analyses. The new models will be solved using multiplicative analysis techniques, and the results will be compared with classical analysis. With this new model, it is planned to clarify the results obtained in the classical case, to reveal more clearly the relationship between the size of the cell and nutrient absorption and consumption in the cell membrane, and to obtain important results.