Simulação numérica de modelo fracionário para a difusão mássica de fármacos na pele humana e estimativa do coeficiente de difusão mássica e da ordem do modelo via algoritmos genéticos

Abstract

The aim of this paper was to study the diffusion of drug through human skin by means of numerical simulation and mathematical modelling. The mathematical modelling utilized was of integer and non-integer order, furthermore, genetic algorithm (GA) was utilized to estimate simultaneously the order of fractional derivative and the diffusion coefficient. The entire coding was made by the author in the MATLab platform, it does mean that optimization function was not used. By means of the analyses was possible conclude that: the implementation of the whole algorithm was correct enabling to notice the importance of elitism and mutation in GA; there was not significant variation of solution quality when the type of crossover was changed; the fractional derivative is a powerful tool to adjusting complex equations that cannot be described by classical models; and, the conclusion was that the algorithm implemented proved to be efficient at solving the problem of this paper, resulting in small residuals, on order of 10-8.