Similarity Solutions for Keller-Segel model with fractional diffusion of cells

In this paper, the similarity method has been used to solve fractional Keller-Segel model where the diffusion is represented by a nonlocal fractional Laplace operator. In order to verify the results, fractional centred difference method and weighted shifted Grüwald-Letnikov difference method have been employed for reduction equations. The comparison of results establishes the accuracy and efficiency of the proposed two numerical schemes.