<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Fractional analysis has evolved considerably over the last decades and has become popular in many technical and scientific fields. Many integral operators which ables us to integrate from fractional orders has been generated. Each of them provides different properties such as semigroup property, singularity problems etc. In this paper, firstly, we obtained a new kernel, then some new integral inequalities which are valid for integrals of fractional orders by using Riemann-Liouville fractional integral. To do this, we used some well-known inequalities such as Hölder's inequality or power mean inequality. Our results generalize some inequalities exist in the literature.</p>
</abstract>

Fractional analysis has evolved considerably over the last decades and has become popular in many technical and scientific fields. Many integral operators which ables us to integrate from fractional orders has been generated. Each of them provides different properties such as semigroup property, singularity problems etc. In this paper, firstly, we obtained a new kernel, then some new integral inequalities which are valid for integrals of fractional orders by using Riemann-Liouville fractional integral. To do this, we used some well-known inequalities such as Hölder's inequality or power mean inequality. Our results generalize some inequalities exist in the literature.

Some new inequalities for convex functions via Riemann-Liouville fractional integrals

Department of Elemenatary Mathematics Education, Faculty of Education

Department of Mathematics, K.K. Faculty of Education

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fractional analysis has evolved considerably over the last decades and has become popular in many technical and scientific fields. Many integral operators...

Some new inequalities for convex functions via Riemann-Liouville fractional integrals

Published Online: Jun 30, 2020

Page range: 537 - 544

Received: Jul 09, 2019

Accepted: Jan 14, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00015

Keywords
Riemann-Liouville, Fractional calculus, Convexity

© 2020 Mustafa Gürbüz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Some new inequalities for convex functions via Riemann-Liouville fractional integrals

Published Online: Jun 30, 2020

Page range: 537 - 544

Received: Jul 09, 2019

Accepted: Jan 14, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00015

KeywordsRiemann-Liouville, Fractional calculus, Convexity

© 2020 Mustafa Gürbüz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Riemann-Liouville, Fractional calculus, Convexity