Bibliography

This website concerns the systems of non-Newtonian calculus, multiplicative calculus, and nonclassical arithmetic created by Michael Grossman and Robert Katz between 1967 and 1970. The website was last edited on 24 June 2021. 


[1] Dorota Aniszewska. "Multiplicative Runge-Kutta methods", Nonlinear Dynamics, Volume 50, 1-2, Springer,  2007.

[2] Agamirza E. Bashirov, Emine Misirli Kurpinar, and Ali Ozyapici. "Multiplicative calculus and its applications", Journal of Mathematical Analysis and Applications, Volume 337, Issue 1, pages 36 - 48,  http://dx.doi.org/10.1016/j.jmaa.2007.03.081, Elsevier, January 2008. 

[3] Fernando Córdova-Lepe. "From quotient operation toward a proportional calculus", Journal of Mathematics, Game Theory and Algebra, 2004. (Also, please see [105].)

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[5]  Non-Newtonian Calculus and Related Matters: Eight Books (Full-View), HathiTrust, https://babel.hathitrust.org/cgi/mb?a=listis;c=216746186%7C%3Cem%3ENon-Newtonian.

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[7] Jane Grossman. Meta-Calculus: Differential and Integral , ISBN 0977117022, 1981. 

[8] Jane Grossman, Michael Grossman, and Robert Katz. Averages: A New Approach,  ISBN 0977117049, 1983.

[9] Jane Grossman, Michael Grossman, Robert Katz. The First Systems of Weighted Differential and Integral Calculus, ISBN 0977117014, 1980.

[10] Michael Grossman. Bigeometric Calculus: A System with a Scale-Free Derivative, ISBN 0977117030, 1983.

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[94] Agamirza E. Bashirov, Emine Misirli, Yucel Tandogdu, and Ali Ozyapici. "On modeling with multiplicative differential equations", HAL Id: hal-0094578,  Applied Mathematics - A Journal of Chinese Universities, Volume 26, Number 4, pages 425-428, ISSN: 1993-0445, DOI:10.1007/s11766-011-2767-6, China Society for Industrial and Applied Mathematics, Springer, 2011.

[95] Agamirza E. Bashirov and Mustafa Riza. "On complex multiplicative differentiation", TWMS Journal of Applied and Engineering Mathematics, Volume 1, Number 1, pages 75-85, 2011.

[96] Luc Florack. "Regularization of positive definite matrix fields based on multiplicative calculus", Reference 9, Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, Volume 6667/2012, pages 786-796, DOI: 10.1007/978-3-642-24785-9_66, Springer, 2012.

[97] Stanley Paul Palasek. "Nonlinear modeling and optimization of peptide delivery", Intel® International Science and Engineering Fair, PH029, Society for Science and the Public, 2011.

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[105] F. Córdova-Lepe and M. Pinto. "From quotient operation toward a proportional calculus", International Journal of Mathematics, Game Theory and Algebra, Volume 18, Number 6, pages 527-536, 2009. 

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[108] Sergey P. Verevkin, Vladimir N. Emel'yanenko, Ingo Krossing, and Roland Kalb. "Thermochemistry of ammonium based ionic liquids: tetra-alkyl ammonium nitrates - experiments and computations", The Journal of Chemical Thermodynamics, Volume 51, pages 107–113, http://dx.doi.org/10.1016/j.jct.2012.02.035, Elsevier, 2012.

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[110] Mathematics Department of Eastern Mediterranean University in North Cyprus. Research Group: Multiplicative Calculus.

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[122] Ahmet Faruk Cakmak and Feyzi Basar. "Some new results on sequence spaces with respect to non-Newtonian calculus", Journal of Inequalities and Applications, SpringerOpen, 2012:228, doi:10.1186/1029-242X-2012-228, October of 2012.

[123] Emine Misirli and Yusuf Gurefe. "The new numerical algorithms for solving multiplicative differential equations", International Conference of Mathematical Sciences, Maltepe University, Istanbul, Turkey, 04-10 August 2009.

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[128] Muttalip Ozavsar and Adem Cengiz Cevikel. "Fixed points of multiplicative contraction mappings on multiplicative metric spaces", arXiv preprint arXiv:1205.5131, 2012.   

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[130] Dorota Aniszewska and Marek Rybaczuk. "Analysis of the multiplicative Lorenz system", Chaos, Solitons & Fractals, Volume 25, Issue 1, pages 79 - 90, Elsevier, 2005.

[131] Dorota Aniszewska and Marek Rybaczuk. "Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems", Nonlinear Dynamics, Volume 54, Issue 4, Springer, 2008.

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[136] Inonu University, Computer Engineering Department. Master's Degree, 2013.

[137] Zafer Cakir. "Spaces of continuous and bounded functions over the field of non-Newtonian complex numbers", lecture at The Algerian-Turkish International Days on Mathematics, University of Badji Mokhtar at Annaba, Algeria, October of 2012.

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