Recently, we considered the $g$-subdiffusion equation with a fractional Caputo time derivative with respect to another function $g$, T. Kosztołowicz et al. [Phys. Rev. E 104, 014118 (2021)]. This equation offers different possibilities for modeling diffusion such as a process in which a type of diffusion evolves continuously over time. However, the equation has not been derived from a stochastic model and the stochastic interpretation of $g$ subdiffusion is still unknown. In this Letter, we show the stochastic foundations of this process. We derive the equation by means of a modified continuous time random walk model. An interpretation of the $g$-subdiffusion process is also discussed.

Close

PrevNext

View figure in article

• Diffusion
• Mathematical physics
• Random walks