This work introduces fractional d-bar derivatives in the setting of quaternionic analysis, by giving meaning to fractional powers of the quaternionic d-bar derivative. The definition is motivated by starting from nth-order d-bar derivatives for \(n\in {\mathbb {N}}\), and further justified by various natural properties such as composition laws and its action on special functions such as Fueter polynomials.

中文翻译：

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四元数 d-Bar 导数的分数幂

这项工作通过赋予四元数 d-bar 导数的分数幂意义，在四元数分析的背景下引入了分数 d-bar 导数。该定义的动机是从\(n\in {\mathbb {N}}\)的n阶 d-bar 导数开始，并通过各种自然属性（例如组合定律及其对特殊函数（例如富特多项式。