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.

回顾了度量和分布的分数阶导数和积分。重点是平移不变分数算子的域和共域。分数阶导数和积分被解释为具有幂律核的卷积算子，被发现具有最大的定义域。因此，通过卷积算子将域从函数扩展到分布有助于对许多先前存在的分数积分和导数定义进行深远的统一。因此，Weyl 分数算子可以使用伴随方法扩展到分布。此外，离散分数阶微积分和周期分布的分数阶微积分都可以用以下形式表示和理解： -卷积。