A Generalized Diffusion Equation: Solutions and Anomalous Diffusion

We investigate the solutions of a generalized diffusion-like equation by considering a spatial and time fractional derivative and the presence of non-local terms, which can be related to reaction or adsorption-desorption processes. We use the Green function approach to obtain solutions and evaluate the spreading of the system to show a rich class of behaviors. We also connect the results obtained with the anomalous diffusion processes.

Automated summary

In this study, the solutions of a generalized diffusion-like equation are investigated, taking into account spatial and time fractional derivatives as well as non-local terms. The Green function approach is used to obtain solutions and analyze the spreading of the system, revealing a diverse range of behaviors. The obtained results are also connected to anomalous diffusion processes.