The concept of derivative is an old concept and there are numerous studies on this concept. Some of these studies are on fractional order derivative. In this paper, we will emphasize that the methods for fractional order derivative are not valid for chain rule, and all definitions for fractional order derivatives have some deficiencies, since the basic concepts of these definitions are based on the pseudo-continuity and gamma function derived from classical derivation. Due to this case, a new definition for chain rule in fractional order derivative was improved. The validity of definition was verified by theorems and examples.
| Published in | Science Innovation (Volume 3, Issue 6) |
| DOI | 10.11648/j.si.20150306.11 |
| Page(s) | 63-67 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
Fractional Calculus, Derivative, Fractional Order Derivatives, Chain Rule
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APA Style
Ali Karci. (2015). Chain Rule for Fractional Order Derivatives. Science Innovation, 3(6), 63-67. https://doi.org/10.11648/j.si.20150306.11
ACS Style
Ali Karci. Chain Rule for Fractional Order Derivatives. Sci. Innov. 2015, 3(6), 63-67. doi: 10.11648/j.si.20150306.11
AMA Style
Ali Karci. Chain Rule for Fractional Order Derivatives. Sci Innov. 2015;3(6):63-67. doi: 10.11648/j.si.20150306.11
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Download@article{10.11648/j.si.20150306.11,
author = {Ali Karci},
title = {Chain Rule for Fractional Order Derivatives},
journal = {Science Innovation},
volume = {3},
number = {6},
pages = {63-67},
doi = {10.11648/j.si.20150306.11},
url = {https://doi.org/10.11648/j.si.20150306.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.si.20150306.11},
abstract = {The concept of derivative is an old concept and there are numerous studies on this concept. Some of these studies are on fractional order derivative. In this paper, we will emphasize that the methods for fractional order derivative are not valid for chain rule, and all definitions for fractional order derivatives have some deficiencies, since the basic concepts of these definitions are based on the pseudo-continuity and gamma function derived from classical derivation. Due to this case, a new definition for chain rule in fractional order derivative was improved. The validity of definition was verified by theorems and examples.},
year = {2015}
}
TY - JOUR T1 - Chain Rule for Fractional Order Derivatives AU - Ali Karci Y1 - 2015/09/24 PY - 2015 N1 - https://doi.org/10.11648/j.si.20150306.11 DO - 10.11648/j.si.20150306.11 T2 - Science Innovation JF - Science Innovation JO - Science Innovation SP - 63 EP - 67 PB - Science Publishing Group SN - 2328-787X UR - https://doi.org/10.11648/j.si.20150306.11 AB - The concept of derivative is an old concept and there are numerous studies on this concept. Some of these studies are on fractional order derivative. In this paper, we will emphasize that the methods for fractional order derivative are not valid for chain rule, and all definitions for fractional order derivatives have some deficiencies, since the basic concepts of these definitions are based on the pseudo-continuity and gamma function derived from classical derivation. Due to this case, a new definition for chain rule in fractional order derivative was improved. The validity of definition was verified by theorems and examples. VL - 3 IS - 6 ER -
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