具有Caputo分数阶导数的次扩散方程
Subdiffusion equation with Caputo fractional derivative with respect to another function
摘要：
我们展示了一个应用程序的子扩散方程与Caputo分数阶时间导数相对于另一个功能$g$描述子扩散介质中具有随时间演变的结构。在这种情况下，可以发生从次扩散到其他类型的扩散的连续过渡。该过程可以被解释为具有固定亚扩散参数（亚扩散指数）$α$的“普通”亚扩散，其中时间尺度由函数$g$改变。作为例子，我们考虑从“普通”亚扩散到超低扩散的过渡。函数$g$生成叠加在由“普通”子扩散生成的“标准”老化上的附加老化过程。老化过程分析使用系数的相对老化的$g$ -亚扩散相对于“普通”亚扩散。给出了求解$g$ -亚扩散方程的方法。
英文摘要：
We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function $g$ to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition from subdiffusion to other type of diffusion may occur. The process can be interpreted as "ordinary" subdiffusion with fixed subdiffusion parameter (subdiffusion exponent) $α$ in which time scale is changed by the function $g$. As example, we consider the transition from "ordinary" subdiffusion to ultraslow diffusion. The function $g$ generates the additional aging process superimposed on the "standard" aging generated by "ordinary" subdiffusion. The aging process is analyzed using coefficient of relative aging of $g$--subdiffusion with respect to "ordinary" subdiffusion. The method of solving the $g$-subdiffusion equation is also presented.
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