在全空间 Rn 中考虑带有 Hardy 位势的分数阶偏微分方程（ P ）：（-Δ）α2 u（x）＝1xγup （x） x ∈ Rn ，与对应的积分方程 u（ x ）＝ c∫up （y）| x - y |n-α| y |γdy的x ∈ Rn Rn等价性，其中0＜γ＜α＜2＃n，c是常数。采用一种新颖且直接的方法来证明。一旦等价性建立，则对积分方程正解的性质都可以应用到分数阶偏微分方程上面。%We consider the equivalence between the fractional partial differential equation (P) with Hardy term in Rn : (- Δ) α2 u(x) = 1xγup (x) x ∈ Rn ,and the correspondingintegral equation u(x)=U(x) ≥ 0 x ∈ Rn c∫up (y)| x - y | n-α | y |γdy ,where 0 < γ< α< 2 #n and c is a constant .A new and direct approach is Rn employed to prove the equivalence . Once the equivalence is established ,all results of the positive solutions to an integral equation can be applied to the fractional partical difference equation (PDE) .
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