分布的分数微积分

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
R. Hilfer, T. Kleiner
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引用次数: 0

摘要

回顾了度量和分布的分数导数和积分。重点是平移不变分数算子的域和共域。发现被解释为具有幂律核的卷积算子的分数导数和积分具有最大的定义域。因此,通过卷积算子将域从函数扩展到分布,有助于深远地统一许多先前存在的分数积分和导数定义。因此,Weyl 小数算子利用邻接法扩展到了分布。此外,离散化分数微积分和周期性分布的分数微积分都可以用卷积来表述和理解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Fractional calculus for distributions

Fractional calculus for distributions

Fractional derivatives and integrals for measures and distributions are reviewed. The focus is on domains and co-domains for translation invariant fractional operators. Fractional derivatives and integrals interpreted as -convolution operators with power law kernels are found to have the largest domains of definition. As a result, extending domains from functions to distributions via convolution operators contributes to far reaching unifications of many previously existing definitions of fractional integrals and derivatives. Weyl fractional operators are thereby extended to distributions using the method of adjoints. In addition, discretized fractional calculus and fractional calculus of periodic distributions can both be formulated and understood in terms of -convolution.

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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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