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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 isdoi:10.1016/j.jksus.2015.03.007 fatcat:exs7ipcvkndllnfwsanq7ugblm