Kosztołowicz Tadeusz
Institute of Physics, Jan Kochanowski University, Uniwersytecka 7, 25-406 Kielce, Poland.
Phys Rev E. 2023 Jul;108(1-1):014132. doi: 10.1103/PhysRevE.108.014132.
An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann-Liouville type which is a differential-integral operator with the kernel defined by the Laplace transform; the kernel controls the immobilization process. We propose a method for calculating the inverse Laplace transform providing the kernel in the time domain. In the long time limit the subdiffusion-immobilization process reaches a stationary state in which the probability density of a particle distribution is an exponential function.
通过连续时间随机游走模型推导了一个描述粒子可能固定化的亚扩散方程。该方程包含黎曼 - 刘维尔型分数阶时间导数，它是一个具有由拉普拉斯变换定义的核的微分 - 积分算子；该核控制着固定化过程。我们提出了一种计算逆拉普拉斯变换的方法，以在时域中得到该核。在长时间极限下，亚扩散 - 固定化过程达到一个稳态，其中粒子分布的概率密度是一个指数函数。
