Sobolev框架下分数阶导数的链式法则

IF 0.9 4区数学 Q2 MATHEMATICS Mathematical Inequalities & Applications Pub Date : 2021-04-11 DOI:10.7153/mia-2021-24-77

K. Fujiwara

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引用次数: 2

摘要

研究了Sobolev空间框架下分数阶微分算子幂乘积的链式法则。分数阶微分算子由傅里叶乘数定义。当微分算子的阶数在1和2之间时，链式法则被重新考虑。该研究是基于对经典链式法则或莱布尼茨法则的类比。

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Remark on the Chain rule of fractional derivative in the Sobolev framework

A chain rule for power product is studied with fractional differential operators in the framework of Sobolev spaces. The fractional differential operators are defined by the Fourier multipliers. The chain rule is considered newly in the case where the order of differential operators is between one and two. The study is based on the analogy of the classical chain rule or Leibniz rule.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.