I am studying some papers about the fractional laplacian, and I am stuck on a formula that I do not understand. I would like to ask if anybody can give me some help. In this paper, on page 12, there is a formula for the Green function $G_\alpha$ of a problem in $1+1$ dimensions. However, in this paper by Xavier Cabré, it seems to me that the Green function should have a completely different form, as noticed in Remarks 3.8 and 3.10. In particular, I do not understand the presence of an exponential term in the paper by Kenig. So my question is: what is the relationship between the function $G_\alpha$ of the first paper and the functions appearing in Remarks 3.8 and 3.10 of the second paper?
Green's function for fractional operators
0
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pde
fractional-calculus