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

Hijaz Ahmad,Muhammad Tariq,Soubhagya Kumar Sahoo,Sameh Askar,Khaled Mohamed Khedher,Ahmed E Abouelregal

doi:10.3390/sym13112059

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.

Highlights

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
The fundamental objective of this article is to set up the Ostrowski-type inequalities for convex functions involving the Atangana–Baleanu fractional operator
The majority of the results introduced are refinements of the overall composition of the current results for new and classical convex functions

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Fractional derivatives and fractional integrals have received significant interest among researchers. Fractional derivatives and fractional integrals provide more exact models of the frameworks than classical derivative and integrals do. Numerous utilizations of fractional calculus in bioengineering, electrochemical processes, modeling of viscoelastic damping, dielectric polarization, and various branches of sciences could be found in [1,2,3,4]

Objectives

Results

Conclusion