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

In this article, first, we deduce an equality involving the Atangana–Baleanu (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">AB</mi></semantics></math></inl...

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Autores principales:	Hijaz Ahmad, Muhammad Tariq, Soubhagya Kumar Sahoo, Sameh Askar, Ahmed E. Abouelregal, Khaled Mohamed Khedher
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Ostrowski inequality Hölder inequality power mean inequality Young’s inequality Atangana–Baleanu fractional integral operator convex function Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ae822c9f8f044b7dac2de6d769d34e54
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spelling	oai:doaj.org-article:ae822c9f8f044b7dac2de6d769d34e542021-11-25T19:06:24ZRefinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator10.3390/sym131120592073-8994https://doaj.org/article/ae822c9f8f044b7dac2de6d769d34e542021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2059https://doaj.org/toc/2073-8994In this article, first, we deduce an equality involving the Atangana–Baleanu (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">AB</mi></semantics></math></inline-formula>)-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>\|</mo><mi mathvariant="sans-serif">Υ</mi><mo>\|</mo></mrow></semantics></math></inline-formula>. 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.Hijaz AhmadMuhammad TariqSoubhagya Kumar SahooSameh AskarAhmed E. AbouelregalKhaled Mohamed KhedherMDPI AGarticleOstrowski inequalityHölder inequalitypower mean inequalityYoung’s inequalityAtangana–Baleanu fractional integral operatorconvex functionMathematicsQA1-939ENSymmetry, Vol 13, Iss 2059, p 2059 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Ostrowski inequality Hölder inequality power mean inequality Young’s inequality Atangana–Baleanu fractional integral operator convex function Mathematics QA1-939
spellingShingle	Ostrowski inequality Hölder inequality power mean inequality Young’s inequality Atangana–Baleanu fractional integral operator convex function Mathematics QA1-939 Hijaz Ahmad Muhammad Tariq Soubhagya Kumar Sahoo Sameh Askar Ahmed E. Abouelregal Khaled Mohamed Khedher Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
description	In this article, first, we deduce an equality involving the Atangana–Baleanu (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">AB</mi></semantics></math></inline-formula>)-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>\|</mo><mi mathvariant="sans-serif">Υ</mi><mo>\|</mo></mrow></semantics></math></inline-formula>. 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.
format	article
author	Hijaz Ahmad Muhammad Tariq Soubhagya Kumar Sahoo Sameh Askar Ahmed E. Abouelregal Khaled Mohamed Khedher
author_facet	Hijaz Ahmad Muhammad Tariq Soubhagya Kumar Sahoo Sameh Askar Ahmed E. Abouelregal Khaled Mohamed Khedher
author_sort	Hijaz Ahmad
title	Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
title_short	Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
title_full	Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
title_fullStr	Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
title_full_unstemmed	Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator
title_sort	refinements of ostrowski type integral inequalities involving atangana–baleanu fractional integral operator
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ae822c9f8f044b7dac2de6d769d34e54
work_keys_str_mv	AT hijazahmad refinementsofostrowskitypeintegralinequalitiesinvolvingatanganabaleanufractionalintegraloperator AT muhammadtariq refinementsofostrowskitypeintegralinequalitiesinvolvingatanganabaleanufractionalintegraloperator AT soubhagyakumarsahoo refinementsofostrowskitypeintegralinequalitiesinvolvingatanganabaleanufractionalintegraloperator AT samehaskar refinementsofostrowskitypeintegralinequalitiesinvolvingatanganabaleanufractionalintegraloperator AT ahmedeabouelregal refinementsofostrowskitypeintegralinequalitiesinvolvingatanganabaleanufractionalintegraloperator AT khaledmohamedkhedher refinementsofostrowskitypeintegralinequalitiesinvolvingatanganabaleanufractionalintegraloperator
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Refinements of Ostrowski Type Integral Inequalities Involving Atangana–Baleanu Fractional Integral Operator

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