Proceedings of the 2016 International Conference on Education, Management and Computer Science

Comparison of Definition of Several Fractional Derivatives

Authors
Yun Ouyang, Wusheng Wang
Corresponding Author
Yun Ouyang
Available Online May 2016.
DOI
https://doi.org/10.2991/icemc-16.2016.114How to use a DOI?
Keywords
Riemann-Liouville fractional derivatives; Caputo's fractional derivative; Grunwald- Letnikov fractional derivatives; Fractional integral.
Abstract
The idea of fractional derivatives was raised first by L'Hospital in 1695. The fractional calculus and its mathematical consequences attracted many mathematicians such as Fourier, Euler, Laplace. Various definitions of non-integer order integral or derivative was given by many mathematicians. In this paper, firstly, we discuss the positive integer higher order derivative of a function, and obtain general formula of high order derivative. Secondly, we introduce the definitions of Grunwald-Letnikov, Riemann-Liouville and Caputo. Finally, we point out the relationship between these definitions. Caputo's integral definition and Grunwald-Letnikov integral definition are consistent with the Riemann-Liouville integral definition. When f has m+1 order continuous derivative and m
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Proceedings
2016 International Conference on Education, Management and Computer Science
Part of series
Advances in Intelligent Systems Research
Publication Date
May 2016
ISBN
978-94-6252-202-2
ISSN
1951-6851
DOI
https://doi.org/10.2991/icemc-16.2016.114How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Yun Ouyang
AU  - Wusheng Wang
PY  - 2016/05
DA  - 2016/05
TI  - Comparison of Definition of Several Fractional Derivatives
BT  - 2016 International Conference on Education, Management and Computer Science
PB  - Atlantis Press
SN  - 1951-6851
UR  - https://doi.org/10.2991/icemc-16.2016.114
DO  - https://doi.org/10.2991/icemc-16.2016.114
ID  - Ouyang2016/05
ER  -