Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the the...

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Autores principales:	Soubhagya Kumar Sahoo, Muhammad Tariq, Hijaz Ahmad, Ayman A. Aly, Bassem F. Felemban, Phatiphat Thounthong
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	convex function Hermite-Hadamard inequality h-convex function Riemann-Liouville <i>k</i>-fractional integrals Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d9abdd6353064fe0a1feea967f9b8f6a
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id	oai:doaj.org-article:d9abdd6353064fe0a1feea967f9b8f6a
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spelling	oai:doaj.org-article:d9abdd6353064fe0a1feea967f9b8f6a2021-11-25T19:07:36ZSome Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings10.3390/sym131122092073-8994https://doaj.org/article/d9abdd6353064fe0a1feea967f9b8f6a2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2209https://doaj.org/toc/2073-8994The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the <i>k</i>-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how <b>q</b>-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.Soubhagya Kumar SahooMuhammad TariqHijaz AhmadAyman A. AlyBassem F. FelembanPhatiphat ThounthongMDPI AGarticleconvex functionHermite-Hadamard inequalityh-convex functionRiemann-Liouville <i>k</i>-fractional integralsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2209, p 2209 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	convex function Hermite-Hadamard inequality h-convex function Riemann-Liouville <i>k</i>-fractional integrals Mathematics QA1-939
spellingShingle	convex function Hermite-Hadamard inequality h-convex function Riemann-Liouville <i>k</i>-fractional integrals Mathematics QA1-939 Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Ayman A. Aly Bassem F. Felemban Phatiphat Thounthong Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
description	The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the <i>k</i>-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how <b>q</b>-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.
format	article
author	Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Ayman A. Aly Bassem F. Felemban Phatiphat Thounthong
author_facet	Soubhagya Kumar Sahoo Muhammad Tariq Hijaz Ahmad Ayman A. Aly Bassem F. Felemban Phatiphat Thounthong
author_sort	Soubhagya Kumar Sahoo
title	Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
title_short	Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
title_full	Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
title_fullStr	Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
title_full_unstemmed	Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings
title_sort	some hermite–hadamard-type fractional integral inequalities involving twice-differentiable mappings
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d9abdd6353064fe0a1feea967f9b8f6a
work_keys_str_mv	AT soubhagyakumarsahoo somehermitehadamardtypefractionalintegralinequalitiesinvolvingtwicedifferentiablemappings AT muhammadtariq somehermitehadamardtypefractionalintegralinequalitiesinvolvingtwicedifferentiablemappings AT hijazahmad somehermitehadamardtypefractionalintegralinequalitiesinvolvingtwicedifferentiablemappings AT aymanaaly somehermitehadamardtypefractionalintegralinequalitiesinvolvingtwicedifferentiablemappings AT bassemffelemban somehermitehadamardtypefractionalintegralinequalitiesinvolvingtwicedifferentiablemappings AT phatiphatthounthong somehermitehadamardtypefractionalintegralinequalitiesinvolvingtwicedifferentiablemappings
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Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings

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