Multiplicative Dirac System

Abstract

We define a Dirac system in multiplicative calculus by some algebraic structures. Asymptotic estimates for eigenfunctions of the multiplicative Dirac system are obtained. Eventually, some fundamental properties of the multiplicative Dirac system are examined in detail.

A non-Newtonian magnetic curves in multiplicative Riemann manifolds

“…Also, Bashirov A. et al reconsider multiplicative analysis with some basic definitions, theorems, propositions, properties and examples [17]. The multiplicative Dirac system and multiplicative time scale are studied by Yilmaz E. et al [18][19][20]. Georgiev S. introduced a highly unconventional perspective to multiplicative analysis through her publications in 2022 [21][22][23].…”

Miscellaneous properties of Sturm-Liouville problems in multiplicative calculus

“…Since several events in the real world such as the magnitudes of earthquakes, the levels of sound signals and the acidities of chemicals change exponentially, geometric calculus which is defined as multiplicative calculus provides a great benefit. Multiplicative calculus is convenient for some problems, e.g., in applied mathematics [1,3,4,6,19,28,29], mathematical analysis [6,15,19,21,24,30], spectral analysis [11,14,31], physics [10,22], biology [16,17], economics and finance [7,8], medicine [9], pattern recognition in images [18] and signal processing [20]. In recent years, multiplicative calculus has received a lot of attention, and most of the published research has been interested in some problems of differential equation, integral equation, spectral analysis, mathematical analysis.…”

“…Important results have been obtained on Sturm-Liouville equations by many researchers over the years. Recently, some spectral properties of Sturm-Liouville problems in multiplicative calculus have been studied by many authors [11,14,31]. In [11], the author has moved a special S-L problem in the usual case to multiplicative calculus in the aspect of spectral analysis.…”

Some Approaches for Solving Multiplicative Second-Order Linear Differential Equations with Variable Exponentials and Multiplicative Airy’s Equation

“…Up until the beginning of the 2000s, relatively little research had been done on this analysis. Numerous studies have recently been conducted on it, and the results are of high quality and effectiveness (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). Using the fundamental ideas of multiplicative analysis, various investigations on multiplicative ordinary differential equations have been conducted in recent years [18][19][20][21][22].…”