This paper solves the Dirichlet boundary value problem of distinguishing domains for Clifford fractional–monogenic functions in \(\mathbb {R}^{n}\) for fixed n, in the Riemann–Liouville sense. To do so, we use a matrix representation of the Clifford algebras. This allows us to construct computational algorithms that efficiently perform the calculations necessary to guarantee the existence of a solution for the Dirichlet boundary value problem over a properly distinguished domain. Finally, we show some explicit solutions for the Dirichlet boundary problem in \(\mathbb {R}^{3}\).

中文翻译：

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Riemann-Liouville意义上的分数单项函数的Dirichlet边值问题

本文解决了在区分域为克利福分数单基因功能的狄利克雷边界值问题\（\ mathbb {R} ^ {N} \）固定Ñ，在黎曼-刘维感。为此，我们使用Clifford代数的矩阵表示。这使我们能够构建能够有效执行必要计算的计算算法，以保证在适当区分的域上存在Dirichlet边值问题的解决方案。最后，我们给出\（\ mathbb {R} ^ {3} \）中Dirichlet边界问题的一些显式解。