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Validities of Fractional Order Derivatives in Literatures Such as Riemann-Liouville, Euler, Caputo and Grünwald-Letnikov

Year 2021, , 166 - 171, 01.12.2021
https://doi.org/10.53070/bbd.982188

Abstract

In this paper, it has been proven that it would be more accurate to accept Euler, Riemann-Liouville, Caputo, and Grünwald-Letnikov methods as curve fitting or amplitude shifting methods without derivative definition

References

  • Newton, I. Philosophiæ Naturalis Principia Mathematica; Jussu Societatis Regiae ac Typis Joseph Streater. Prostat apud plures bibliopolas: London, UK, 1687.
  • L’Hôpital, G. Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes (Infinitesimal Calculus with Applications to Curved Lines); François Montalant: Paris, France, 1696.
  • L’Hôpital, G. Analyse des Infinement Petits; Relnk Books: Paris, France, 1715.
  • Das, S.,Functional fractional calculus, Springer, 2011.
  • Hatcher, W.S., The Logical Foundations of Mathematics, Pergamon Press, 1982.
  • Karcı, A.,”Kesirli Türev için Yapılan Tanımlamaların Eksiklikleri ve Yeni Yaklaşım”, TOK-2013 Turkish Automatic Control National Meeting and Exhibition, 2013a.
  • Karcı,A., “A New Approach for Fractional Order Derivative and Its Applications”, Universal Journal of Engineering Sciences, Vol:1, pp: 110-117, 2013b.
  • Karcı, A., “Properties of Fractional Order Derivatives for Groups of Relations/Functions”, Universal Journal of Engineering Sciences, vol:3, pp:39-45, 2015a.
  • Karcı,A., “The Properties of New Approach of Fractional Order Derivative”, Journal of the Faculty of Engineering and Architecture of Gazi University, Vol.30, pp:487-501, 2015b.
  • Karcı, A.,” Fractional order entropy New perspectives”, Optik - International Journal for Light and Electron Optics, Vol:127, pp:9172-9177, 2016.
  • Karcı, A.,” Malatya Functions: Symmetric Functions Obtained by Applying Fractional Order Derivative to Karcı Entropy”, Anatolian Science Journal of Computer Sciences, Vol:2, pp:1-8, 2017.
  • Karcı, A.,” Properties of Karcı’s Fractional Order Derivative”, Universal Journal of Engineering Science, Vol:7, pp:32-38, 2019.
  • Karcı, A., Karcı, Ş.,” Discovering The Relationships between Fractional Order Derivatives and Complex Numbers”, Anatolian Science - journal of Computer Science, Vol:5, pp:42-53, 2020.

Validities of Fractional Order Derivatives in Literatures Such as Riemann-Liouville, Euler, Caputo and Grünwald-Letnikov

Year 2021, , 166 - 171, 01.12.2021
https://doi.org/10.53070/bbd.982188

Abstract

In this paper, it has been proven that it would be more accurate to accept Euler, Riemann-Liouville, Caputo, and Grünwald-Letnikov methods as curve fitting or amplitude shifting methods without derivative definition

References

  • Newton, I. Philosophiæ Naturalis Principia Mathematica; Jussu Societatis Regiae ac Typis Joseph Streater. Prostat apud plures bibliopolas: London, UK, 1687.
  • L’Hôpital, G. Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes (Infinitesimal Calculus with Applications to Curved Lines); François Montalant: Paris, France, 1696.
  • L’Hôpital, G. Analyse des Infinement Petits; Relnk Books: Paris, France, 1715.
  • Das, S.,Functional fractional calculus, Springer, 2011.
  • Hatcher, W.S., The Logical Foundations of Mathematics, Pergamon Press, 1982.
  • Karcı, A.,”Kesirli Türev için Yapılan Tanımlamaların Eksiklikleri ve Yeni Yaklaşım”, TOK-2013 Turkish Automatic Control National Meeting and Exhibition, 2013a.
  • Karcı,A., “A New Approach for Fractional Order Derivative and Its Applications”, Universal Journal of Engineering Sciences, Vol:1, pp: 110-117, 2013b.
  • Karcı, A., “Properties of Fractional Order Derivatives for Groups of Relations/Functions”, Universal Journal of Engineering Sciences, vol:3, pp:39-45, 2015a.
  • Karcı,A., “The Properties of New Approach of Fractional Order Derivative”, Journal of the Faculty of Engineering and Architecture of Gazi University, Vol.30, pp:487-501, 2015b.
  • Karcı, A.,” Fractional order entropy New perspectives”, Optik - International Journal for Light and Electron Optics, Vol:127, pp:9172-9177, 2016.
  • Karcı, A.,” Malatya Functions: Symmetric Functions Obtained by Applying Fractional Order Derivative to Karcı Entropy”, Anatolian Science Journal of Computer Sciences, Vol:2, pp:1-8, 2017.
  • Karcı, A.,” Properties of Karcı’s Fractional Order Derivative”, Universal Journal of Engineering Science, Vol:7, pp:32-38, 2019.
  • Karcı, A., Karcı, Ş.,” Discovering The Relationships between Fractional Order Derivatives and Complex Numbers”, Anatolian Science - journal of Computer Science, Vol:5, pp:42-53, 2020.
There are 13 citations in total.

Details

Primary Language English
Subjects Computer Software
Journal Section PAPERS
Authors

Ali Karci 0000-0002-8489-8617

Publication Date December 1, 2021
Submission Date August 12, 2021
Acceptance Date October 29, 2021
Published in Issue Year 2021

Cite

APA Karci, A. (2021). Validities of Fractional Order Derivatives in Literatures Such as Riemann-Liouville, Euler, Caputo and Grünwald-Letnikov. Computer Science, 6(3), 166-171. https://doi.org/10.53070/bbd.982188

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