Self-similar Stationary and Time Dependent Solutions of Diffusion Equation in the Presence of an External Field

Instead of the fractional diffusion equation, the Euclidean diffusion equation with an external force field has been solved by means of Lie group approach. We compare our results with those obtained from an alternative description for anomalous diffusion, namely fractional diffusion. With a logarithmic potential one may see that the Euclidean diffusion equation might play a relevant role as a description of anomalous diffusion.