Volume 8, Issue 5, October 2019, Page: 83-87
Classical Properties on Conformable Fractional Calculus
Musraini M., Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Rustam Efendi, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Endang Lily, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Ponco Hidayah, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Received: Sep. 3, 2019;       Accepted: Oct. 9, 2019;       Published: Oct. 23, 2019
DOI: 10.11648/j.pamj.20190805.11      View  30      Downloads  13
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.
Keywords
Fractional Calculus, Conformable Fractional Derivative, Conformable Fractional Integral
To cite this article
Musraini M., Rustam Efendi, Endang Lily, Ponco Hidayah, Classical Properties on Conformable Fractional Calculus, Pure and Applied Mathematics Journal. Vol. 8, No. 5, 2019, pp. 83-87. doi: 10.11648/j.pamj.20190805.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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