Fractional Moisil-Teodorescu operator in elasticity and electromagnetism

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Abstract

In this work, we introduce a fractional generalization of the classical Moisil-Teodorescu operator that provides a concise notation for presenting a mathematical formulation of physical systems in fractional space from various branches of science and engineering. The method used in this article, called the Stillinger's formalism, is combined in a novel way with quaternionic analysis. As a concrete application, a quaternionic reformulation of a fractional time-harmonic Maxwell system is established, thus showing a deep relation between it solutions with those of the perturbed fractional Moisil-Teodorescu operator. Furthermore, the fractional constructions here will find further applications in several applied research areas such as in hydrodynamics and magneto-hydrodynamics.

Original languageEnglish
Pages (from-to)6811-6818
Number of pages8
JournalAlexandria Engineering Journal
Volume61
Issue number9
DOIs
StatePublished - Sep 2022

Keywords

  • Elasticity
  • Electromagnetism
  • Fractional Calculus
  • Fractional Laplacian
  • Fractional Moisil-Teodorescu operator
  • Maxwell system

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