一个四元分数Borel-Pompeiu型公式
A quaternionic fractional Borel-Pompeiu type formula
摘要：
四元数分析在很大程度上依赖于在$\mathbb R^4$（或$\mathbb R^3$）中的域上定义的函数的结果，其值在$\mathbb H$中。该理论围绕着$ψ-$超全纯函数的概念，即，与$\mathbb H^4$的所谓结构集$ψ$相关的$ψ-$ Fueter算子的零解。分数阶微积分，涉及任意实数或复数阶的导数积分，是经典微积分的自然推广，在后来的几年里，它成为许多科学和工程分支研究人员的一个非常合适的工具。在理论上，结合一个依赖于一个附加的分数实部复参数向量的分数$ψ-$ Fueter算子，建立了Borel-Pompeiu公式的分数模拟，作为发展分数$ψ-$超全纯函数理论和相关算子演算的第一步.
英文摘要：
Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or $\mathbb R^3$) with values in $\mathbb H$. This theory is centered around the concept of $ψ-$hyperholomorphic functions i.e., null-solutions of the $ψ-$Fueter operator related to a so-called structural set $ψ$ of $\mathbb H^4$. Fractional calculus, involving derivatives-integrals of arbitrary real or complex order, is the natural generalization of the classical calculus, which in the latter years became a well-suited tool by many researchers working in several branches of science and engineering. In theoretical setting, associated with a fractional $ψ-$Fueter operator that depends on an additional vector of complex parameters with fractional real parts, this paper establishes a fractional analogue of Borel-Pompeiu formula as a first step to develop a fractional $ψ-$hyperholomorphic function theory and the related operator calculus.
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