摘要：The space-fractional Fokker–Planck type equation ∂ p ∂ t + γ ∂ p ∂ x = - D ( - Δ ) α / 2 p ( 0 < α ⩽ 2 ) subject to the initial condition p ( x , 0 ) = δ ( x ) is solved in terms of Fox H functions. The solution as γ = 0 expresses the Lévy stable distribution with the index α . From the properties of Fox H functions, the series representation and asymptotic behavior for the solution are also obtained. Lévy stable distribution as 0 < α < 2 describes anomalous superdiffusion and its diffusion velocity is characterized by x d ∝ ( Dt ) 1 / α .
关键词：Fokker–Planck equation;Laplace operator;Fourier transform;Fox H function
