Subdiffusion equation with Caputo fractional derivative with respect to another function

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) alpha in which timescale is changed by the function g. As an example, we consider the transition from ordinary subdiffusion to ultraslow diffusion. The g-subdiffusion process 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.

Automated summary

The paper demonstrates the application of a subdiffusion equation with Caputo fractional time derivative in describing subdiffusion in a medium with evolving structure. A continuous transition from subdiffusion to other types of diffusion can occur by changing the timescale with the function g. This g-subdiffusion process generates an additional aging process on top of the standard aging process produced by ordinary subdiffusion.