ON RIESZ DERIVATIVE
ON RIESZ DERIVATIVE
复制标题
DOI：
10.1515/fca-2019-0019
复制
发表时间：
2019-04-01
影响因子：
3
通讯作者：
Li, Changpin
中科院分区：
文献类型：
--
作者：
Cai, Min;Li, Changpin
本文主要研究Riesz导数。对一维Riesz导数性质的研究表明，它不同于其它分数阶导数，如Riemann-Liouville导数和Caputo导数。在现有的文献中，Riesz导数通常被认为是R上分数拉普拉斯算子的替代。详细地证明了Riesz导数与分数阶Laplacian算子在n >= 1时的等价性。
This paper focuses on studying Riesz derivative. An interesting investigation on properties of Riesz derivative in one dimension indicates that it is distinct from other fractional derivatives such as Riemann-Liouville derivative and Caputo derivative. In the existing literatures, Riesz derivative is commonly considered as a proxy for fractional Laplacian on R. We show the equivalence between Riesz derivative and fractional Laplacian on R-n with n >= 1 in details.