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A Dirichlet Boundary Value Problem for Fractional Monogenic Functions in the Riemann–Liouville Sense

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Abstract

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 \(\mathbb {R}^{3}\).

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Notes

  1. The simply connected domain \(\Omega \) is given by (1.1).

  2. It is important to emphasize that each component \(u_{A}\) has to satisfy the hypothesis of Theorem 2.7.

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Acknowledgements

The authors would like to thank the reviewers for many useful comments which lead to substantial improvements of the paper. Also, we want to thank Diego Ochoa for the discussions that allowed to improve the paper.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad San Francisco de Quito, Diego de Robles y vía Interoceánica, Quito, Ecuador

    David Armendáriz & Antonio Di Teodoro

  2. Escuela de Ciencias Físicas y Matemáticas, Universidad de Las Américas, Avenida de los Granados y Colimes, Quito, Ecuador

    Johan Ceballos

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  1. David Armendáriz
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  2. Johan Ceballos
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  3. Antonio Di Teodoro
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Correspondence to Antonio Di Teodoro.

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This article is part of the topical collection“Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Armendáriz, D., Ceballos, J. & Di Teodoro, A. A Dirichlet Boundary Value Problem for Fractional Monogenic Functions in the Riemann–Liouville Sense. Complex Anal. Oper. Theory 14, 51 (2020). https://doi.org/10.1007/s11785-020-01008-z

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