$Generalized proportional fractional integral Hermite–Hadamard’s inequalities$
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Generalized proportional fractional integral Hermite–Hadamard’s inequalities

Abstract The theory of fractional integral inequalities plays an intrinsic role in approximation theory also it has been a key in establishing the uniqueness of solutions for some fractional differential equations. Fractional calculus has been found to be the best for modeling physical and engineeri...

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Autores principales:	Tariq A. Aljaaidi, Deepak B. Pachpatte, Thabet Abdeljawad, Mohammed S. Abdo, Mohammed A. Almalahi, Saleh S. Redhwan
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Hermite–Hadamard inequalities Fractional inequalities ψ-proportional fractional operators Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/83fdc9dddacc4c329eb3642433d6ac7e
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id	oai:doaj.org-article:83fdc9dddacc4c329eb3642433d6ac7e
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spelling	oai:doaj.org-article:83fdc9dddacc4c329eb3642433d6ac7e2021-11-14T12:10:30ZGeneralized proportional fractional integral Hermite–Hadamard’s inequalities10.1186/s13662-021-03651-y1687-1847https://doaj.org/article/83fdc9dddacc4c329eb3642433d6ac7e2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03651-yhttps://doaj.org/toc/1687-1847Abstract The theory of fractional integral inequalities plays an intrinsic role in approximation theory also it has been a key in establishing the uniqueness of solutions for some fractional differential equations. Fractional calculus has been found to be the best for modeling physical and engineering processes. More precisely, the proportional fractional operators are one of the recent important notions of fractional calculus. Our aim in this research paper is developing some novel ways of fractional integral Hermite–Hadamard inequalities in the frame of a proportional fractional integral with respect to another strictly increasing continuous function. The considered fractional integral is applied to establish some new fractional integral Hermite–Hadamard-type inequalities. Moreover, we present some special cases throughout discussing this work.Tariq A. AljaaidiDeepak B. PachpatteThabet AbdeljawadMohammed S. AbdoMohammed A. AlmalahiSaleh S. RedhwanSpringerOpenarticleHermite–Hadamard inequalitiesFractional inequalitiesψ-proportional fractional operatorsMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-19 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Hermite–Hadamard inequalities Fractional inequalities ψ-proportional fractional operators Mathematics QA1-939
spellingShingle	Hermite–Hadamard inequalities Fractional inequalities ψ-proportional fractional operators Mathematics QA1-939 Tariq A. Aljaaidi Deepak B. Pachpatte Thabet Abdeljawad Mohammed S. Abdo Mohammed A. Almalahi Saleh S. Redhwan Generalized proportional fractional integral Hermite–Hadamard’s inequalities
description	Abstract The theory of fractional integral inequalities plays an intrinsic role in approximation theory also it has been a key in establishing the uniqueness of solutions for some fractional differential equations. Fractional calculus has been found to be the best for modeling physical and engineering processes. More precisely, the proportional fractional operators are one of the recent important notions of fractional calculus. Our aim in this research paper is developing some novel ways of fractional integral Hermite–Hadamard inequalities in the frame of a proportional fractional integral with respect to another strictly increasing continuous function. The considered fractional integral is applied to establish some new fractional integral Hermite–Hadamard-type inequalities. Moreover, we present some special cases throughout discussing this work.
format	article
author	Tariq A. Aljaaidi Deepak B. Pachpatte Thabet Abdeljawad Mohammed S. Abdo Mohammed A. Almalahi Saleh S. Redhwan
author_facet	Tariq A. Aljaaidi Deepak B. Pachpatte Thabet Abdeljawad Mohammed S. Abdo Mohammed A. Almalahi Saleh S. Redhwan
author_sort	Tariq A. Aljaaidi
title	Generalized proportional fractional integral Hermite–Hadamard’s inequalities
title_short	Generalized proportional fractional integral Hermite–Hadamard’s inequalities
title_full	Generalized proportional fractional integral Hermite–Hadamard’s inequalities
title_fullStr	Generalized proportional fractional integral Hermite–Hadamard’s inequalities
title_full_unstemmed	Generalized proportional fractional integral Hermite–Hadamard’s inequalities
title_sort	generalized proportional fractional integral hermite–hadamard’s inequalities
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/83fdc9dddacc4c329eb3642433d6ac7e
work_keys_str_mv	AT tariqaaljaaidi generalizedproportionalfractionalintegralhermitehadamardsinequalities AT deepakbpachpatte generalizedproportionalfractionalintegralhermitehadamardsinequalities AT thabetabdeljawad generalizedproportionalfractionalintegralhermitehadamardsinequalities AT mohammedsabdo generalizedproportionalfractionalintegralhermitehadamardsinequalities AT mohammedaalmalahi generalizedproportionalfractionalintegralhermitehadamardsinequalities AT salehsredhwan generalizedproportionalfractionalintegralhermitehadamardsinequalities
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Generalized proportional fractional integral Hermite–Hadamard’s inequalities

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