This article discusses the use of hereditary models of radon volumetric activity (RVA) to describe the dynamics of radon accumulation in a storage chamber, taking into account the memory effects in the process of radon transport. Hereditary RVA models represent a generalization of classical concepts and mathematical models of the RVA process, based on ODEs, to FDEs with Gerasimov-Caputo fractional derivative of variable-order \(0<\alpha(t)<1\) . The main focus of the article is on the modification of hereditary RVA models to account, among other things, for the parameter τ, which is associated with a certain characteristic time, the time scale of the dynamic process. This is related to the fact that replacing the ordinary derivative in the model equation with a fractional operator cannot go unnoticed in terms of dimensional consistency in such a generalized equation. Therefore, to compensate for the impact of the fractional derivative, a parameter \(\tau\neq 1\) is introduced as a certain positive constant with the dimension of time. The aim of the study is to examine the impact of the parameter τ on the simulation results, specifically the amplitude and duration over time of the model curve of the dynamic RVA process. As a result, it is shown that the introduction of the parameter \(\tau \neq 1\) into the model equation through the coefficient \(\tau^{1-\alpha(t)}\) represents a scaling parameter for the amplitude of the desired solution function of the FDEs. From this, it follows that the introduction of the parameter \(\tau \neq 1\) in hereditary RVA models will be sufficient to maintain the equality of the dimensions of the left and right sides of the fractional model equation.
