On a System of Equations with General Fractional Derivatives Arising in Diffusion Theory

Abstract

A novel two-compartment model for drug release was formulated. The general fractional derivatives of a specific type and distributed order were used in the formulation. Earlier used models in pharmacokinetics with fractional derivatives follow as special cases of the model proposed here. As a first application, we used this model to study the release of gentamicin from poly(vinyl alcohol)/chitosan/gentamicin (PVA/CHI/Gent) hydrogel aimed at wound dressing in the medical treatment of deep chronic wounds. As a second application, we studied the release of gentamicin from antibacterial biodynamic hydroxyapatite/poly(vinyl alcohol) /chitosan/gentamicin (HAP/PVA/CS/Gent) coating on a titanium substrate for bone tissue implants, which enables drug delivery directly to the infection site. In both cases. a good agreement is obtained between the measured data and the data calculated from the model proposed here. The form of the general fractional derivatives used here results in an additional parameter in the compartmental model used here. This, as a consequence, leads to a better approximation of the experimental data with only a slightly more complicated numerical procedure in obtaining the solution.