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

Yıl 2021, Cilt: 6 Sayı: 3, 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, Cilt: 6 Sayı: 3, 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 Cilt: 6 Sayı: 3

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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