TY  - JOUR
T1  - Validities of Fractional Order Derivatives in Literatures Such as Riemann-Liouville, Euler, Caputo and Grünwald-Letnikov
TT  - Validities of Fractional Order Derivatives in Literatures Such as Riemann-Liouville, Euler, Caputo and Grünwald-Letnikov
AU  - Karci, Ali
PY  - 2021
DA  - December
Y2  - 2021
DO  - 10.53070/bbd.982188
JF  - Computer Science
JO  - JCS
PB  - Ali KARCI
WT  - DergiPark
SN  - 2548-1304
SP  - 166
EP  - 171
VL  - 6
IS  - 3
LA  - en
AB  - 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
KW  - Fractional order derivatives
KW  - Grünwald-Letnikov derivative
KW  - Riemann-Liouville derivative
KW  - Caputo derivative
N2  - 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
CR  - Newton, I. Philosophiæ Naturalis Principia Mathematica; Jussu Societatis Regiae ac Typis Joseph Streater. Prostat apud plures bibliopolas: London, UK, 1687.
CR  - 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.
CR  - L’Hôpital, G. Analyse des Infinement Petits; Relnk Books: Paris, France, 1715.
CR  - Das, S.,Functional fractional calculus, Springer, 2011.
CR  - Hatcher, W.S., The Logical Foundations of Mathematics, Pergamon Press, 1982.
CR  - Karcı, A.,”Kesirli Türev için Yapılan Tanımlamaların Eksiklikleri ve Yeni Yaklaşım”, TOK-2013 Turkish Automatic Control National Meeting and Exhibition, 2013a.
CR  - Karcı,A., “A New Approach for Fractional Order Derivative and Its Applications”, Universal Journal of Engineering Sciences, Vol:1, pp: 110-117, 2013b.
CR  - Karcı, A., “Properties of Fractional Order Derivatives for Groups of Relations/Functions”, Universal Journal of Engineering Sciences, vol:3, pp:39-45, 2015a.
CR  - 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.
CR  - Karcı, A.,” Fractional order entropy  New perspectives”,  Optik - International Journal for Light and Electron Optics, Vol:127, pp:9172-9177, 2016.
CR  - 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.
CR  - Karcı, A.,” Properties of Karcı’s Fractional Order Derivative”,  Universal Journal of Engineering Science, Vol:7, pp:32-38, 2019.
CR  - 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.
UR  - https://doi.org/10.53070/bbd.982188
L1  - https://dergipark.org.tr/en/download/article-file/1922328
ER  -