Mass transport in brain cells: integer-order and fractional-order modeling

Abstract This work successfully elucidates the process of mass transport to brain tissues in a mathematical framework by considering two concepts of porosity and tortuosity in terms of both integer-order and fractional-order models. Henceforth, the analytical solutions to the mass transport model are also obtained to find the response functions by means of which the transport process becomes quite explicit. For better insight into the transport process, a graphical analysis is taken into account. The newly-developed fractional version not only presents better-suited analytical solutions to the model but additionally the graphs also show the matching of the solutions for both integer-order and fractional models. Based on the approximation for four sets of experimental data made by the analytical solution through the means of graphical and numerical results, the fractional model also leads to the selection of the best possible values of the fractional order. We also establish the credibility of the fractional-order model in approximating a wide class of experimental data taken from the laboratory. All the observations clearly establish the superiority of fractional model over the integer-order one.