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Several New Integral Inequalities via Caputo $k$ -Fractional Derivative Operators

Saad Ihsan Butt

Comsats University Islamabad, Lahore Campus, Pakistan

E-mail Address: saadihsanbutt@gmail.com

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M. Emin Özdemir

Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey

E-mail Address: eminozdemir@uludag.edu.tr

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Muhammad Umar

Comsats University Islamabad, Lahore Campus, Pakistan

E-mail Address: umarqureshi987@gmail.com

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, and

Bariş Çeli̇k

Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey

Department of Mathematics Education, Education Faculty, Bursa Uludağ University, Görükle Campus, Bursa, Turkey

E-mail Address: bariscelik15@hotmail.com

Corresponding author.

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https://doi.org/10.1142/S1793557121501503Cited by:1 (Source: Crossref)

Abstract

In this paper, we establish several new integral inequalities involving Caputo $k$ -fractional derivatives for $η$ -quasi-convex and $s$ -Godunova–Levin convex. In order to obtain our results, we use some classical inequalities such as Hölder’s inequality and its power mean and weighted versions.

Communicated by J. Pecaric

Keywords:

AMSC: 26A33, 26D10, 26D15

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