On the fractional Laplacian of variable order

被引：6
|
作者：
Darve, Eric [1 ,2 ]
D'Elia, Marta [3 ]
Garrappa, Roberto [4 ,5 ]
Giusti, Andrea [6 ]
Rubio, Natalia L. [2 ]
机构：
[1] Stanford Univ, Inst Computat & Math Engn, Stanford, CA 94305 USA
[2] Stanford Univ, Dept Mech Engn, Stanford, CA 94305 USA
[3] Sandia Natl Labs, Computat Sci & Anal, Livermore, CA USA
[4] Univ Bari, Dept Math, Via E Orabona 4, I-0126 Bari, Italy
[5] INdAM Res Grp GNCS, Rome, Italy
[6] Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2022年 / 25卷 / 01期
关键词：
Variable-order fractional Laplacian; Fourier transform;
D O I：
10.1007/s13540-021-00003-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a novel definition of variable-order fractional Laplacian on R-n based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson's equation involving this operator and we compute the corresponding Green's function, for which we provide some instructive examples for specific problems.
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页码：15 / 28
页数：14
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