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Journals / Fundamentals of Contemporary Mathematical Sciences / 2024 / Volume: 5 Issue: 2

ϕ−Multiplicative Calculus

Orhan Dişkaya(MERSIN UNIVERSITY)0000-0001-5698-7834
Pages
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Publication Date
2024-07-31
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

The paper contributes to the academic discourse by providing a comprehensive exploration of the proposed ϕ-multiplicative calculus, presenting a robust foundation for further investigations in this specialized mathematical domain.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present a novel mathematical framework termed “ϕ-multiplicative calculus”, which serves as a Golden Fibonacci calculus to fundamental concepts in multiplicative calculus.
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Key Findings & Data:This innovative calculus introduces a parameter ϕ (Golden ratio), offering a nuanced extension of traditional calculus.
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Conclusion & Impact:The paper contributes to the academic discourse by providing a comprehensive exploration of the proposed ϕ-multiplicative calculus, presenting a robust foundation for further investigations in this specialized mathematical domain.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci numbers · multiplicative derivative · golden calculus

Abstract

In this paper, we present a novel mathematical framework termed “ϕ-multiplicative calculus”, which serves as a Golden Fibonacci calculus to fundamental concepts in multiplicative calculus. This innovative calculus introduces a parameter ϕ (Golden ratio), offering a nuanced extension of traditional calculus. Our work encompasses the establishment of ϕ-multiplicative calculus and the demonstration of essential theorems concerning derivatives, integrals, and their operation properties within this mathematical framework. The paper contributes to the academic discourse by providing a comprehensive exploration of the proposed ϕ-multiplicative calculus, presenting a robust foundation for further investigations in this specialized mathematical domain.

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Cite This Article

Dişkaya, O. (2024). ϕ−Multiplicative Calculus. Fundamentals of Contemporary Mathematical Sciences, Volume: 5 Issue: 2. https://doi.org/10.54974/fcmathsci.1412066

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References (22)

  1. Bashirov A.E., Kurpınar E.M., Özyapıcı A., Multiplicative calculus and its applications, Journal of Mathematical Analysis and Applications, 337(1), 36-48, 2008.
  2. Bashirov A., Rıza M., On complex multiplicative differentiation, TWMS Journal of Applied and Engineering Mathematics, 1, 75-85, 2011.
  3. Bashirov A., On line and double multiplicative integrals, TWMS Journal of Applied and Engineering Mathematics, 3(1), 103-107, 2013.
  4. Boyer C.B., Merzbach U.C., A History of Mathematics, John Wiley & Sons, 2011.
  5. Calinger R.S., Leonhard Euler: Mathematical Genius in the Enlightenment, Princeton University Press, 2015.
  6. Florack L., Assen H.V., Multiplicative calculus in biomedical image analysis, Journal of Mathematical Imaging and Vision, 42, 64-75, 2012.
  7. Georgiev S.G., Zennir K., Multiplicative Differential Calculus, CRC Press, Boca Raton, 2023.
  8. Göktaş S., Yilmaz E., Yar A.C., Multiplicative derivative and its basic properties on time scales, Mathematical Methods in the Applied Sciences, 45(4), 2097-2109, 2022.
  9. Gurefe Y., Multiplicative Differential Equations and Its Applications, Master Thesis, Ege University, Institute of Sciences, İzmir, Türkiye, 2013.
  10. Grossman M., Katz R., Non-Newtonian Calculus, Lee Press, Pigeon Cove, 1972.
  11. Kac V.G., Cheung P., Quantum Calculus (Vol. 113), Springer, 2002.
  12. Koshy T., Fibonacci and Lucas Numbers with Applications (Vol. 1)„ John Wiley & Sons, 2018.
  13. Krot E., An introduction to finite fibonomial calculus, Open Mathematics, 2(5), 754-766, 2004.
  14. Kuş S., Tuğlu N., Kim T., Bernoulli F−polynomials and Fibo–Bernoulli matrices, Advances in Difference Equations, 145, 1-16, 2019.
  15. Misirli E., Gurefe Y., Multiplicative adams bashforth–moulton methods, Numerical Algorithms, 57, 425-439, 2011.
  16. Mora M., Córdova-Lepe F., Del-Valle R., A non-Newtonian gradient for contour detection in images with multiplicative noise, Pattern Recognition Letters, 33(10), 1245-1256, 2012.
  17. Özvatan M., Generalized Golden-Fibonacci Calculus and Applications, Master Thesis, İzmir Institute of Technology, Türkiye, 2018.
  18. Pashaev O.K., Nalci S., Golden quantum oscillator and Binet–Fibonacci calculus. Journal of Physics A: Mathematical and Theoretical, 45(1), 015303, 2011.
  19. Riza M., Özyapici A., Misirli E., Multiplicative finite difference methods, Quarterly of Applied Mathematics, 67(4), 745-754, 2009.
  20. Sadjang P.N., On the fundamental theorem of (p, q)−calculus and some (p, q)−Taylor formulas, Results in Mathematics, 73, 1-21, 2018.
  21. Stanley D., A multiplicative calculus, Problems, Resources, and Issues in Mathematics Undergraduate Studies, 9(4), 310-326, 1999.
  22. Yener G., Emiroğlu T., A q−analogue of the multiplicative calculus: q−multiplicative calculus, Discrete and Continuous Dynamical Systems, 8(6), 1435-1450, 2015.