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

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

Öz

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

Kaynakça

  • 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

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

Öz

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

Kaynakça

  • 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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Bilgisayar Yazılımı
Bölüm PAPERS
Yazarlar

Ali Karci 0000-0002-8489-8617

Yayımlanma Tarihi 1 Aralık 2021
Gönderilme Tarihi 12 Ağustos 2021
Kabul Tarihi 29 Ekim 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

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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