Comparison of Definition of Several Fractional Derivatives
- Yun Ouyang, Wusheng Wang
- Corresponding Author
- Yun Ouyang
Available Online May 2016.
- https://doi.org/10.2991/icemc-16.2016.114How to use a DOI?
- Riemann-Liouville fractional derivatives; Caputo's fractional derivative; Grunwald- Letnikov fractional derivatives; Fractional integral.
- 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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- 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 -