Lévy stable distribution and space-fractional Fokker–Planck type equation

Jun-Sheng Duan, Temuer Chaolu, Zhong Wang, Shou-Zhong Fu
2016 Journal of King Saud University: Science  
The space-fractional Fokker-Planck type equation @p @t þ c @p @x ¼ ÀDðÀDÞ a=2 p ð0 < a 6 2Þ subject to the initial condition pðx; 0Þ ¼ dðxÞ is solved in terms of Fox H functions. The solution as c ¼ 0 expresses the Le´vy stable distribution with the index a. From the properties of Fox H functions, the series representation and asymptotic behavior for the solution are also obtained. Le´vy stable distribution as 0 < a < 2 describes anomalous superdiffusion and its diffusion velocity is
more » ... ed by x d / ðDtÞ 1=a . ª 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
doi:10.1016/j.jksus.2015.03.007 fatcat:exs7ipcvkndllnfwsanq7ugblm