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.

引用

页码：15 / 28

页数：14

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