Subdiffusion equation with Caputo fractional derivative with respect to another function
| Autor: | Kosztołowicz, Tadeusz, Dutkiewicz, Aldona |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 104, 014118 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.104.014118 |
| Popis: | 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 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. Comment: 9 pages, 7 figures |
| Databáze: | arXiv |
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