Solutions for a fractional diffusion equation with noninteger dimensions

Solutions for a fractional diffusion equation with noninteger dimensions

L. S. Lucena, L. R. da Silva, A. A. Tateishi, M. K. Lenzi, H. V. Ribeiro, E. K. Lenzi, Nonlinear Analysis: Real World Applications 13, 1955 (2012). PDF | DOI

We investigate a fractional diffusion equation with a nonlocal reaction term by using the Green function approach. We also consider a modified spatial operator in order to cover situations characterized by a noninteger dimension. The results show a nonusual spreading of the initial condition which can be connected to a rich class of anomalous diffusive processes.