Unveiling the dynamics of plasma dilution in medical science through analytical and numerical approaches via fractional integro-differential equations

This study introduces a rigorous mathematical analysis utilizing a fractional integro-differential equation model to depict the intricate dynamics of plasma dilution and provide a comprehensive understanding of its implications in various biomedical and clinical contexts. The integro-differential equation governing plasma dilution is formulated by employing Caputo fractional operators and it is addressed and examined using analytical and numerical techniques, Laplace transform which gives an accurate results for the proposed equation and the composite trapezoidal rule with finite difference method as a numerical approach to validate the proposed model, offering a practical tool for predicting plasma dilution under divers. We also discussed the existence and the uniqueness of solutions. Whereas this model has effectively been utilized with real data obtained from a previous human investigation of thyroid surgery, the graphical illustrations are being presented to clarify the results obtained during two time periods, the infusion and postinfusion periods, the two periods are considered a sequential events the infusion phase transpired within the initial 30 min of the surgical procedure following this, the postinfusion phase extended from 30 min to a limited time.