Two Types of q‐Gaussian Distributions Used to Study the Diffusion in a Finite Region

Abstract

In this work, we explore both the ordinary (Formula presented.) -Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the (Formula presented.) -deformed diffusion differential equation. This approach allows us to realize that the standard deviation of the distribution must be a function of time. In one case, we derive a linear Fokker-Planck equation within a finite region, revealing a new form of both the position- and time-dependent diffusion coefficient and the corresponding continuity equation. It is noteworthy that, in both cases, the conventional result is obtained when (Formula presented.) tends to zero. Furthermore, we derive the deformed diffusion-decay equation in a finite region, also determining the position- and time-dependent decay coefficient. A discrete version of this diffusion-decay equation is addressed, in which the discrete times have a uniform interval, while for the discrete positions, the interval is not uniform.