Two compartmental fractional derivative model with general fractional derivative

Abstract

This study presents a new two compartmental model with, recently defined General fractional derivative. We review that concept of General fractional derivative and use the kernel function that generalizes the classical Caputo derivative in a mathematically consistent way. Next we use this model to study the release of antibiotic gentamicin in poly (vinyl alcohol)/gentamicin(PVA/Gent) hydrogel aimed for wound dressing in medical treatment of deep chronical wounds. The PVA/Gent hydrogel was prepared by physical cross linking of poly (vinyl alcohol) dispersion using freezing-thawing method, and then was swollen in gentamicin solution at 37 °C during 48 h. The concentration of released gentamicin was determined using a high-performance liquid chromatography coupled with mass spectrometer. The advantage of this model is the existence of new parameters in the definition of fractional derivative, as compared with classical fractional compartmental models. The model proposed here in the special case reduces to the classical (integer order) linear two compartmental model as well as classical fractional order two compartmental model since it has more parameters that are determined from the experimental results.

Keywords: Fractional kinetics; General fractional derivative; Gentamicin; Hydrogel.