Work

A Non-integer Dimensional Space Approach to the Moisil-Teodorescu Operator

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2606.30350

Authors: Bory-Reyes, Juan, la Rosa, Marco Antonio Pérez-de, González-Cervantes, José Oscar, Napoles-Valdes, Juan Eduardo

Institutions: Instituto Politécnico Nacional, Universidad de las Américas Puebla, National University of the Northeast

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Instituto Politécnico Nacional

OpenAlex ID: W7166704091

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Cited by: 1

Related to: 10