A Generalized Diffusion Equation: Solutions and Anomalous Diffusion

Abstract

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.

Keywords

• fractional dynamics
• heterogeneity
• unusual spreading
• diffusion process
• flow