jum Journal of Universal Mathematics 2618-5660 2618-5660 Gökhan ÇUVALCIOĞLU 10.33773/jum.1411844 Algebraic and Differential Geometry Operator Algebras and Functional Analysis Cebirsel ve Diferansiyel Geometri Operatör Cebirleri ve Fonksiyonel Analiz PLANE KINEMATICS IN LORENTZIAN HOMOTHETIC MULTIPLICATIVE CALCULUS https://orcid.org/0000-0002-7732-8173 Es Hasan GAZİ ÜNİVERSİTESİ, GAZİ EĞİTİM FAKÜLTESİ 07 31 2024 7 2 64 74 12 29 2023 01 31 2024 Copyright © 2018, Journal of Universal Mathematics 2018 Journal of Universal Mathematics

In this study, Lorentzian plane homothetic multiplicative calculus kinematics is discussed.Lorentzian plane homothetic multiplicative calculus movement, the pole points of a point X relative tothe moving and fixed plane are discussed. In this motion, the velocities and accelerations of a pointX are obtained. In this motion, the relations between the velocities and accelerations of a point X areobtained. In addition, new theorems and results are given.

 Lorentzian homothetic multiplicative one-parameter motion Lorentzian multiplicative pole orbits Lorentzian mulltiplicative speeds and accelerations. V. Volterra, B. Hostinsky, Operations Innitesimales Lineares. Herman, Paris (1938). D. Aniszewska, Multiplicative Runge-Kutta Methods. Nonlinear Dynamics Vol.50, pp.262-272 (2007). W. Kasprzak, B. Lysik, M. Rybaczuk, Dimensions, Invariants Models and Fractals, Ukrainian Society on Fracture Mechanics, Spolom, Wroclaw-Lviv, Poland (2004). M. Rybaczuk, A. Kedzia, W. Zielinski, The concepts of physical and fractional dimensions 2. The differential calculus in dimensional spaces, Chaos Solitons Fractals Vol.12, pp.2537-2552 (2001). M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts (1972). D. Stanley, A multiplicative calculus, Primus IX, Vol.4, pp.310-326 (1999). A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008). S. Aslan, M. Bekar, Y. Yaylı, Geometric 3-space and multiplicative quaternions, International Journal 1 of Geometric Methods in Modern Physics, Vol.20, No.9 (2023). S. Nurkan, K., I. Gürgil, M. K., Karacan, Vector properties of geometric calculus, Math. Meth. Appl. Sci., pp.1-20 (2023). H. Es, On The 1-Parameter Motions With Multiplicative Calculus, Journal of Science and Arts, Vol.2, No.59 (2022). A. E. Bashirov, M. Rıza, On Complex multiplicative differentiation, TWMS J. App. Eng. Math. Vol.1, No.1, pp.75-85 (2011). A. E. Bashirov, E. Mısırlı, Y. Tandoğdu, A. Ozyapıcı, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Vol.26, No.4, pp.425-438 (2011). A. E. Bashirov, E. M. Kurpınar, A. Ozyapici, Multiplicative Calculus and its applications, J. Math. Anal. Appl. Vol.337, pp.36-48 (2008). K. Boruah and B. Hazarika, Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces, arXiv:1603.09479v1 (2016). K. Boruah and B. Hazarika, Some basic properties of G-Calculus and its applications in numerical analysis, arXiv:1607.07749v1(2016). A. F. Çakmak, F. Başar, On Classical sequence spaces and non-Newtonian calculus, J. Inequal. Appl. 2012, Art. ID 932734, 12 pages (2012). E. Misirli and Y. Gurefe, Multiplicative Adams BashfortMoulton methods, Numer Algor, Vol.57, pp.425-439(2011). A. F. Çakmak, F. Başar, Some sequence spaces and matrix transformations in multiplicative sense, TWMS J. Pure Appl. Math. Vol.6, No.1, pp.27-37 (2015). D. Campbell, Multiplicative Calculus and Student Projects, Vol.9, No.4, pp.327-333 (1999) M. Coco, Multiplicative Calculus, Lynchburg College, Vol.9, No.4, pp.327-333 (2009). M. Grossman, Bigeometric Calculus: A System with a scale-Free Derivative, Archimedes Foundation, Massachusetts (1983). M. Grossman, An Introduction to non-Newtonian calculus, Int. J. Math. Educ. Sci. Technol., Vol.10, No.4, pp.525-528 (1979). J. Grossman, M. Grossman, R. Katz, The First Systems of Weighted Differential and Integral Calculus, University of Michigan (1981). J. Grossman, Meta-Calculus: Differential and Integral, University of Michigan (1981). Y. Gurefe, Multiplicative Differential Equations and Its Applications, Ph.D. in Department of Mathematics (2013). W. F. Samuelson, S.G. Mark, Managerial Economics, Seventh Edition (2012). S. Tekin, F. Başar, Certain Sequence spaces over the non-Newtonian complexeld, Abstr. Appl. Anal. Article ID 739319, 11 pages (2013). C. Türkmen and F. Başar, Some Basic Results on the sets of Sequences with Geometric Calculus, Commun. Fac. Fci. Univ. Ank. Series A1., Vol.61, No.2, pp.17-34 (2012). A. Uzer, Multiplicative type Complex Calculus as an alternative to the classical calculus, Comput. Math. Appl. Vol.60, pp.2725-2737 (2010). K. Boruah and B. Hazarika, G-Calculus, TWMS J. App. Eng. Math., Vol.8, No.1, pp.94-105 (2018)