Proportional Pressure--Volume Controlled Artificial Respiration Model on Time Scales

Dynamic problems involving the mechanical model of respiratory devices prepared based on the working principle of the lung bring a different perspective to the current situation in clinical medicine in case the time scale changes. This paper delves into mathematical models performed by delta derivative and proportional derivative on arbitrary time scale for the instantaneous volume in the single compartment lung. Firstly, these problems are solved with appropriate methods. Finally, results are supported on graphical representations of the equations to assess how well the operators mentioned perform in real-world problems and statistical analysis of selected arbitrary values is performed.