发表机构
Instituto Politécnico Nacional; University of Transport and Communications（国立理工学院; 交通与通信大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对四元数分数阶 Cauchy-Riemann 算子，引入适应仿射变换的分数阶超全纯函数类，证明其协变性，并推广了 Stokes、Borel-Pompeiu 和 Cauchy 公式。
AI 中文摘要
本文继续发展四元数函数理论的基础，该理论与作用于四元数函数的分数阶比例 Cauchy-Riemann 型算子相关。我们引入了一类新的分数阶超全纯函数，使其适应于区域的仿射变换，并研究了相应的四元数右模结构。特别地，我们为该函数理论建立了 Stokes、Borel-Pompeiu 和 Cauchy 公式的版本。我们证明了该分数阶算子在仿射变换下的协变性质，表明与仿射映射的复合，并乘以适当的四元数因子，保持了分数阶超全纯函数的类别。结果表明，该结果包含了作者先前考虑的情形，并将其协变性质推广到仿射变换的设定中。
英文摘要
In this paper, we continue the development of the foundations of a quaternionic function theory that is associated to a fractional proportional Cauchy-Riemann type operator acting on quaternionic functions. We introduce a new class of fractional hyperholomorphic functions adapted to affine transformations of the domain, and study the corresponding quaternionic right module structure. In particular, we establish versions of the Stokes, Borel-Pompeiu and Cauchy formulas for this function theory. A covariance property of the fractional operator under affine transformations is proved, showing that the composition with an affine map, weighted by a suitable quaternionic factor, preserves the class of fractional hyperholomorphic functions. The result is shown to include the case considered previously by the authors, and extends their covariance property to the setting of affine transformations.
