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arXiv · 2308.15655

A bicomplex proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator using Riemann-Liouville derivatives with respect to an hyperbolic-valued function

José Oscar González-Cervantes·Juan Adrián Ramírez-Belman·Juan Bory-Reyes
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Abstract

Based on the Riemann-Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a novel bicomplex proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, involving weights hyperbolic orthogonal bicomplex functions. This operator is defined for the first time here, and its associated fractional Borel-Pompeiu formula is proved as the main result.

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José Oscar González-Cervantes, Juan Adrián Ramírez-Belman, Juan Bory-Reyes. 2023-08-29. A bicomplex proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator using Riemann-Liouville derivatives with respect to an hyperbolic-valued function. https://arxiv.org/abs/2308.15655

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