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Abstract
This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts.
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D Aniszewska.Multiplicative Runge-Kutta method, Nonlinear Dynamics, 2007, 50(1–2): 265–272.
A Bashirov, E Kurpınar, A özyapıcı.Multiplicative calculus and its applications, Journal of Mathematical Analysis and Its Applications, 2008, 337(1): 36–48.
A Bashirov, G Bashirova.Dynamics of literary texts and diffusion, Online Journal of Communication and Media Technologies, 2011, 1(3): 60–82.
A Bashirov, M Riza.On complex multiplicative differentiation, TWMS Journal on Applied and Engineering Mathematics, 2011, 1(1): 75–85.
A Bashirov, M Riza.Complex multiplicative calculus, arXiv: 1103.1462v1.
F Córdova-Lepe.The multiplicative derivative as a measure of elasticity in economics, TEMAT-Theaeteto Atheniensi Mathematica, 2006, 2(3): online.
F Córdova-Lepe, M Pinto.From quotient operation toward a proportional calculus, International Journal of Mathematics, Game Theory and Algebra, 2009, 18(6): 527–536.
J Englehardt, J Swartout, C Loewenstine.A new theoretical discrete growth distribution with verification for microbial counts in water, Risk Analysis, 2009, 29(6): 841–856.
D A Filip, C Piatecki.A non-Newtinian examination of the theory of exogenous economic growth, CNCSIS-UEFISCSU (project no. PNII DEI 2366/2008) and Laboratorie d’Economie d’Orleans, 2010.
L Florack, H van Assen.Multiplicative calculus in biomedical image analysis, Journal of Mathematical Imaging and Vision, doi: 10.1007/s10851-011-0275-1.
B Gompertz.On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philosophical Transactions of the Royal Society of London, 1825, 115: 513–585.
M Grossman, R Katz.Non-Newtonian Calculus, Pigeon Cove, Lee Press, Massachusats, 1972.
M Grossman.Bigeometric Calculus: A System with a Scale-Free Derivative, Archimedes Foundation, Rockport, Massachusats, 1983.
W Kasprzak, B Lysik, M Rybaczuk.Dimensions, Invariants Models and Fractals, Ukrainian Society on Fracture Mechanics, SPOLOM, Wroclaw-Lviv, Poland, 2004.
J R Meginniss.Non-Newtonian calculus applied to probability, utility, and Bayesian analysis, Manuscript of the report for delivery at the 20th KDKR-KSF Seminar on Bayesian Inference in Econometrics, Purdue University, West Lafayette, Indiana, May 2–3, 1980.
M Riza, A Özyapıcı, E Kurpınar.Multiplicative finite difference methods, Quarterly of Applied Mathematics, 2009, 67(4): 745–754.
M Rybaczuk, A Kedzia, W Zielinski.The concepts of physical and fractional dimensions II. The differential calculus in dimensional spaces, Chaos Solutions Fractals, 2001, 12: 2537–2552.
D Stanley.A multiplicative calculus, Primus, 1999, IX(4): 310–326.
A Uzer.Multiplicative type complex calculus as an alternative to the classical calculus, Computers and Mathematics with Applications, 2010, 60(10): 2725–2737.
V Volterra, B Hostinsky.Operations Infinitesimales Lineares, Gauthier-Villars, Paris, 1938.
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Authors and Affiliations
Department of Mathematics, Eastern Mediterranean University, Gazimagusa, via Mersin 10, Turkey
Agamirza E. Bashirov & Yücel Tandoğdu
Department of Mathematics, Ege University, Izmir, Turkey
Emine Mısırlı
Department of Computer Engineering, Lefke European University, Gemikonaǧı, via Mersin 10, Turkey
Ali Özyapıcı
- Agamirza E. Bashirov
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- Emine Mısırlı
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- Yücel Tandoğdu
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- Ali Özyapıcı
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Correspondence toAgamirza E. Bashirov.
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Supported by B-type project MEKB-09-05.
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Bashirov, A.E., Mısırlı, E., Tandoğdu, Y.et al. On modeling with multiplicative differential equations.Appl. Math. J. Chin. Univ.26, 425–438 (2011). https://doi.org/10.1007/s11766-011-2767-6
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