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Plasma dilution is an important factor of a human proteome specifically from hemostatic balance to coagulation process. This manuscript presents a mathematical analysis of integro-differential equation model of plasma dilution model. The integro-differential equation of plasma dilution is modeled via three types of fractional operators namely Atangana-Baleanu, Caputo and Caputo-Fabrizio based on the comparison of non-singular and non-local kernels. The fractionalized integro-differential equation of plasma dilution is solved by invoking Laplace transform method corresponding with physical conditions on plasma dilution model. The lengthy and cumbersome calculations of governing equation namely integro-differential equation of plasma dilution is expressed in the format of generalized hyper-geometric functionand elementary functions. The graphical illustration for plasma dilution model has been depicted for embedded parameters as involved in the governing equation. The comparative analysis of three types of fractional approaches showed a good adaptability in describing pharmacokinetic responses which reflect the crystalloid infusion period as well.

A comparative analysis of plasma dilution based on fractional integro-differential equation: an application to biological science