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A Non-integer Dimensional Space Approach to the Moisil-Teodorescu Operator
Abstract
The vector calculus in non-integer dimensional space (NIDS), including the NIDS version of the standard vector differential operators (gradient, divergence, and curl) is well-known. A deformation of the quaternionic Moisil-Teodorescu operator, written in terms of NIDS derivatives is the main purpose of this article. Along similar lines, we consider the NIDS reformulation of the quaternionic Bitsadze operator and the Lamé-Navier operator of the three-dimensional elasticity theory. Also, a quaternionic reformulation of a NIDS time-harmonic Maxwell system is introduced, whose solutions are directly related with those of the perturbed NIDS Moisil-Teodorescu operator. Finally, a generalized approach to the study is addressed.
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BibTeX
@misc{boryreyes2026noninteger,
title = {{A Non-integer Dimensional Space Approach to the Moisil-Teodorescu Operator}},
author = {Juan Bory-Reyes and Marco Antonio Pérez-de la Rosa and José Oscar González-Cervantes and Juan Eduardo Napoles-Valdes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.30350},
eprint = {2606.30350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30350},
}
RIS
TY - UNPB
TI - A Non-integer Dimensional Space Approach to the Moisil-Teodorescu Operator
AU - Juan Bory-Reyes
AU - Marco Antonio Pérez-de la Rosa
AU - José Oscar González-Cervantes
AU - Juan Eduardo Napoles-Valdes
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2606.30350
UR - https://arxiv.org/abs/2606.30350
AB - The vector calculus in non-integer dimensional space (NIDS), including the NIDS version of the standard vector differential operators (gradient, divergence, and curl) is well-known. A deformation of the quaternionic Moisil-Teodorescu operator, written in terms of NIDS derivatives is the main purpose of this article. Along similar lines, we consider the NIDS reformulation of the quaternionic Bitsadze operator and the Lamé-Navier operator of the three-dimensional elasticity theory. Also, a quaternionic reformulation of a NIDS time-harmonic Maxwell system is introduced, whose solutions are directly related with those of the perturbed NIDS Moisil-Teodorescu operator. Finally, a generalized approach to the study is addressed.
ER -