The paper "About parameter of the characteristic time scale in hereditary models of radon volumetric activity" has been published in Computational Mathematics and Modeling Journal by Springer

The authors are the Researcher of the Laboratory of Electromagnetic Radiation of IKIR FEB RAS, Cand. Sci. (Phys.-Math.) Tverdiy Dmitriy Aleksandrovich; Chief Researcher of the Laboratory of Physical Process Modeling, Dr. Sci. (Phys.-Math.) Parovik Roman Ivanovich.

The paper presents an investigation addressing the issues of maintaining the dimensions of physical quantities in a model equation based on fractional derivatives of both constant and variable orders. The paper is mainly focused on a class of mathematical hereditary models of radon volumetric activity (RVA) for describing the dynamics of accumulation processes and radon variations in an accumulation chamber taking into account memory effects during radon transfer.

RVA hereditary models generalize the classical model of radon accumulation to estimate RVA based on an ordinary derivative with time. The scientific novelty of the study lies in the introduction of a new dimensionless parameter τ as a similarity parameters, which is related to the time of radon transfer process and has the meaning of dimensionless time. Introduction of such a parameter is associated with the fact that replacing of the ordinary derivative in the model equation with a fractional operator when generalizing the model cannot pass without consequences from the point of view of maintaining the dimensions in the generalized equation.

The aim of the research is to consider the τ effect on the modeling results, in particular, on the amplitude and duration of the RVA model curve. As the result, it was illustrated that introduction of the parameter τ≤1 into the equation by the means of the coefficient, that in its turn is associated with the order of the fractional derivative α(t), is the scaling parameter for the required function of the solution. It follows from the abovesaid that introduction of the parameter τ≤1 into RVA hereditary models will be sufficient to maintain the equality of the left and right parts of the fractional model equation.

Full text of the paper is available here. 

For citation: Tverdyi, D., Parovik, R. About parameter of the characteristic time scale in hereditary models of radon volumetric activity. Comput Math Model (2026). https://doi.org/10.1007/s10598-026-09728-1