Anomalous diffusion of an antibiotic (colistin) in a system consisting of packed gel (alginate) beads immersed in water is studied experimentally and theoretically. The experimental studies are performed using the interferometric method of measuring concentration profiles of a diffusing substance. We use the $g$-subdiffusion equation with the fractional Caputo time derivative with respect to another function $g$ to describe the process. The function $g$ and relevant parameters define anomalous diffusion. We show that experimentally measured time evolution of the amount of antibiotic released from the system determines the function $g$. The process can be interpreted as subdiffusion in which the subdiffusion parameter (exponent) $\alpha$ decreases over time. The $g$-subdiffusion equation, which is more general than the “ordinary” fractional subdiffusion equation, can be widely used in various fields of science to model diffusion in a system in which parameters, and even a type of diffusion, evolve over time. We postulate that diffusion in a system composed of channels and a matrix can be described by the $g$-subdiffusion equation, just like diffusion in a system of packed gel beads placed in water.

• Received 26 August 2021
• Revised 26 April 2022
• Accepted 7 October 2022

DOI:https://doi.org/10.1103/PhysRevE.106.044138