Fractional derivatives with respect to another function in modeling anomalous diffusion processes.
Aldona Dutkiewicz
Adam Mickiewicz Univesity in Poznan, Faculty of Mathematics and Computer Science Poland
Co-Author(s): Tadeusz Kosztolowicz
Abstract:
We will consider the g-subdiffusion equation with the fractional Caputo time derivative with respect to another function g (T. K., A. D., Phys. Rev. E 104, 014118 (2021)). Such equation offers possibilities for modeling diffusion as a process in which a type of diffusion evolves continuously over time (T. K., A. D., Phys. Rev. E 106, 044119 (2022)). The stochastic interpretation of g-subdiffusion will be discussed (T. K., A. D., Phys. Rev. E 104, L042101 (2021)). The method for solving g-subdiffusion equation, based on Laplace-type transform with respect to the function g, will be presented. We also show the application of the g-subdiffusion equation to describe the release of antibiotic from gel beads and its further subdiffusion in a gel system. The g function is then determined by the best fit of theoretical results to empirical data (T. K., A. D. et al., Phys. Rev. E 106, 044138 (2022)).