HIGHER ORDER GRUNWALD APPROXIMATIONS OF FRACTIONAL DERIVATIVES AND FRACTIONAL POWERS OF OPERATORS

被引：34

作者：

Baeumer, Boris ^{[1
]}

Kovacs, Mihaly ^{[1
]}

Sankaranarayanan, Harish ^{[1
]}

机构：

[1] Univ Otago, Dept Math & Stat, Dunedin 9054, New Zealand

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 02期

关键词：

Fractional derivatives; Grunwald formula; Fourier multipliers; Carlson's inequality; fractional differential equations; fractional powers of operators;

D O I：

10.1090/S0002-9947-2014-05887-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give stability and consistency results for higher order Grunwald-type formulae used in the approximation of solutions to fractional-in-space partial differential equations. We use a new Carlson-type inequality for periodic Fourier multipliers to gain regularity and stability results. We then generalise the theory to the case where the first derivative operator is replaced by the generator of a bounded group on an arbitrary Banach space.

引用

页码：813 / 834

页数：22

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