Recently, a definition of fractional which refers to classical calculus form called conformable fractional calculus has been introduced. The main idea of the concept of conformable fractional calculus is how to determine the derivative and integral with fractional order either rational numbers or real numbers. One of the most popular definitions of conformable fractional calculus is defined by Katugampola which is used in this study. This definition satisfies in some respects of classical calculus involved conformable fractional derivative and conformable fractional integral. In the branch of conformable fractional derivatives, some of the additional results such as analysis of fractional derivative in quotient property, product property and Rolle theorem are given. An application on classical calculus such as determining monotonicity of function is also given. Then, in the case of fractional integral, this definition showed that the fractional derivative and the fractional integral are inverses of each other. Some of the classical integral properties are also satisfied on conformable fractional integral. Additionally, this study also has shown that fractional integral acts as a limit of a sum. After that, comparison properties on fractional integral are provided. Finally, the mean value theorem and the second mean value theorem are also applicable for fractional integral.
| Published in | Pure and Applied Mathematics Journal (Volume 8, Issue 5) |
| DOI | 10.11648/j.pamj.20190805.11 |
| Page(s) | 83-87 |
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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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Fractional Calculus, Conformable Fractional Derivative, Conformable Fractional Integral
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APA Style
Musraini M., Rustam Efendi, Endang Lily, Ponco Hidayah. (2019). Classical Properties on Conformable Fractional Calculus. Pure and Applied Mathematics Journal, 8(5), 83-87. https://doi.org/10.11648/j.pamj.20190805.11
ACS Style
Musraini M.; Rustam Efendi; Endang Lily; Ponco Hidayah. Classical Properties on Conformable Fractional Calculus. Pure Appl. Math. J. 2019, 8(5), 83-87. doi: 10.11648/j.pamj.20190805.11
AMA Style
Musraini M., Rustam Efendi, Endang Lily, Ponco Hidayah. Classical Properties on Conformable Fractional Calculus. Pure Appl Math J. 2019;8(5):83-87. doi: 10.11648/j.pamj.20190805.11
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Download@article{10.11648/j.pamj.20190805.11,
author = {Musraini M. and Rustam Efendi and Endang Lily and Ponco Hidayah},
title = {Classical Properties on Conformable Fractional Calculus},
journal = {Pure and Applied Mathematics Journal},
volume = {8},
number = {5},
pages = {83-87},
doi = {10.11648/j.pamj.20190805.11},
url = {https://doi.org/10.11648/j.pamj.20190805.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20190805.11},
abstract = {Recently, a definition of fractional which refers to classical calculus form called conformable fractional calculus has been introduced. The main idea of the concept of conformable fractional calculus is how to determine the derivative and integral with fractional order either rational numbers or real numbers. One of the most popular definitions of conformable fractional calculus is defined by Katugampola which is used in this study. This definition satisfies in some respects of classical calculus involved conformable fractional derivative and conformable fractional integral. In the branch of conformable fractional derivatives, some of the additional results such as analysis of fractional derivative in quotient property, product property and Rolle theorem are given. An application on classical calculus such as determining monotonicity of function is also given. Then, in the case of fractional integral, this definition showed that the fractional derivative and the fractional integral are inverses of each other. Some of the classical integral properties are also satisfied on conformable fractional integral. Additionally, this study also has shown that fractional integral acts as a limit of a sum. After that, comparison properties on fractional integral are provided. Finally, the mean value theorem and the second mean value theorem are also applicable for fractional integral.},
year = {2019}
}
TY - JOUR T1 - Classical Properties on Conformable Fractional Calculus AU - Musraini M. AU - Rustam Efendi AU - Endang Lily AU - Ponco Hidayah Y1 - 2019/10/23 PY - 2019 N1 - https://doi.org/10.11648/j.pamj.20190805.11 DO - 10.11648/j.pamj.20190805.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 83 EP - 87 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20190805.11 AB - Recently, a definition of fractional which refers to classical calculus form called conformable fractional calculus has been introduced. The main idea of the concept of conformable fractional calculus is how to determine the derivative and integral with fractional order either rational numbers or real numbers. One of the most popular definitions of conformable fractional calculus is defined by Katugampola which is used in this study. This definition satisfies in some respects of classical calculus involved conformable fractional derivative and conformable fractional integral. In the branch of conformable fractional derivatives, some of the additional results such as analysis of fractional derivative in quotient property, product property and Rolle theorem are given. An application on classical calculus such as determining monotonicity of function is also given. Then, in the case of fractional integral, this definition showed that the fractional derivative and the fractional integral are inverses of each other. Some of the classical integral properties are also satisfied on conformable fractional integral. Additionally, this study also has shown that fractional integral acts as a limit of a sum. After that, comparison properties on fractional integral are provided. Finally, the mean value theorem and the second mean value theorem are also applicable for fractional integral. VL - 8 IS - 5 ER -
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