On the objectivity of mathematical description of ion transport processes using general temporal Caputo and Riemann-Liouville fractional partial derivatives

Abstract

It is shown that the mathematical description of the ion transport across passive or active biological neuron membrane, voltage propagation along neuron axons and dendrites having passive or active membrane and ion transport in biological neuron networks, using general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, is objective. The basic idea is that different observers using this type of description obtain results which can be reconciled, i.e., transformed into each other using only formulas that link the coordinates of a point in two fixed orthogonal reference frames and the numbers representing a moment of time in two different choices of the origin of time measurement. This requirement was pointed out by Galileo Galilee (1564–1642), Isaac Newton (1643–1727), Albert Einstein (1879–1955) in the context of mathematical description of mechanical movement: “The mechanical event is independent on the observer “.