Kosztołowicz Tadeusz, Dutkiewicz Aldona
Institute of Physics, Jan Kochanowski University, Uniwersytecka 7, 25-406 Kielce, Poland.
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland.
Phys Rev E. 2022 Oct;106(4-1):044119. doi: 10.1103/PhysRevE.106.044119.
A composite subdiffusion equation with fractional Caputo time derivative with respect to another function g is used to describe a process of a continuous transition from subdiffusion with parameters α and D_{α} to subdiffusion with parameters β and D_{β}. The parameters are defined by the time evolution of the mean square displacement of diffusing particle σ^{2}(t)=2D_{i}t^{i}/Γ(1+i), i=α,β. The function g controls the process at intermediate times. The composite subdiffusion equation is more general than the ordinary fractional subdiffusion equation with constant parameters; it has potentially wide application in modeling diffusion processes with changing parameters.
一个关于另一个函数(g)具有分数阶Caputo时间导数的复合次扩散方程，用于描述从具有参数(\alpha)和(D_{\alpha})的次扩散到具有参数(\beta)和(D_{\beta})的次扩散的连续转变过程。这些参数由扩散粒子的均方位移(\sigma^{2}(t)=2D_{i}t^{i}/\Gamma(1 + i))，(i = \alpha,\beta)的时间演化定义。函数(g)控制中间时刻的过程。该复合次扩散方程比具有恒定参数的普通分数阶次扩散方程更具一般性；它在模拟参数变化的扩散过程中具有潜在的广泛应用。
