Stochastic foundations of $g$-subdiffusion process

Abstract

Recently, in the paper: T. Kosztołowicz and A. Dutkiewicz, Phys. Rev. E \textbf{104}, 014118 (2021) the $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ has been considered. This equation offers new possibilities for modelling 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 has been unknown. In this paper we show stochastic foundations of this process. We derive the equation by means of a modified Continuous Time Random Walk model. Interpretation of the $g$--subdiffusion process is also discussed.

4 pages

References in corpus (4)

• A Caputo fractional derivative of a function with respect to another function
• Why the Mittag-Leffler function can be considered the Queen function of the Fractional Calculus?
• The fractional Dodson diffusion equation: a new approach
• Subdiffusion--reaction process with $A⟶B$ reactions versus subdiffusion--reaction process with $A+B⟶B$ reactions