Variational Approach for Solving Oxygen Diffusion Problem with Time-Fractional Derivative

Abstract

One significant problem is the simultaneous absorption and diffusion of oxygen into the cells. When it comes to medical applications, it is crucial. There are two stages to the mathematical formulation of the problem. The stable case in which there is no oxygen transition in the isolated cell is examined in the first stage, and the moving boundary problem pertaining to the oxygen absorbed by the cell's tissues is examined in the second stage. A shifting border is a crucial component of the oxygen diffusion problem. In this paper, we present mathematical model of oxygen diffusion problem with time fractional derivative in Caputo sense. This problem is difficult to solve analytically, so we will use the variational approach to find the corresponding formula for the problem. The well-known Magri's approach formula cannot be used to find a variational formula corresponding to the presented problem, so a modified formula of Magri's approach will be found, and then the corresponding model is solved numerically. So the resulting solution is an approximate analytical solution.