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Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator

Authors :
Hijaz Ahmad
Muhammad Tariq
Soubhagya Kumar Sahoo
Sameh Askar
Ahmed E. Abouelregal
Khaled Mohamed Khedher
Source :
Symmetry, Vol 13, Iss 11, p 2059 (2021)
Publication Year :
2021
Publisher :
MDPI AG, 2021.

Abstract

In this article, first, we deduce an equality involving the Atangana–Baleanu (AB)-fractional integral operator. Next, employing this equality, we present some novel generalization of Ostrowski type inequality using the Hölder inequality, the power-mean inequality, Young’s inequality, and the Jensen integral inequality for the convexity of |Υ|. We also deduced some new special cases from the main results. There exists a solid connection between fractional operators and convexity because of their fascinating properties in the mathematical sciences. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. It is assumed that the results presented in this article will show new directions in the field of fractional calculus.

Details

Language :
English
ISSN :
20738994
Volume :
13
Issue :
11
Database :
Directory of Open Access Journals
Journal :
Symmetry
Publication Type :
Academic Journal
Accession number :
edsdoj.822c9f8f044b7dac2de6d769d34e54
Document Type :
article
Full Text :
https://doi.org/10.3390/sym13112059