Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper...

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Published in:Fractal and Fractional
Main Author: Li H.; Meftah B.; Saleh W.; Xu H.; Kiliçman A.; Lakhdari A.
Format: Article
Language:English
Published: Multidisciplinary Digital Publishing Institute (MDPI) 2024
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196880081&doi=10.3390%2ffractalfract8060345&partnerID=40&md5=43d131148d975d3f1e1c3b7b05962424
id 2-s2.0-85196880081
spelling 2-s2.0-85196880081
Li H.; Meftah B.; Saleh W.; Xu H.; Kiliçman A.; Lakhdari A.
Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
2024
Fractal and Fractional
8
6
10.3390/fractalfract8060345
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196880081&doi=10.3390%2ffractalfract8060345&partnerID=40&md5=43d131148d975d3f1e1c3b7b05962424
This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order (Formula presented.) approaches 1, in addition to the fractional integrals we examined. © 2024 by the authors.
Multidisciplinary Digital Publishing Institute (MDPI)
25043110
English
Article
All Open Access; Gold Open Access
author Li H.; Meftah B.; Saleh W.; Xu H.; Kiliçman A.; Lakhdari A.
spellingShingle Li H.; Meftah B.; Saleh W.; Xu H.; Kiliçman A.; Lakhdari A.
Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
author_facet Li H.; Meftah B.; Saleh W.; Xu H.; Kiliçman A.; Lakhdari A.
author_sort Li H.; Meftah B.; Saleh W.; Xu H.; Kiliçman A.; Lakhdari A.
title Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
title_short Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
title_full Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
title_fullStr Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
title_full_unstemmed Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
title_sort Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
publishDate 2024
container_title Fractal and Fractional
container_volume 8
container_issue 6
doi_str_mv 10.3390/fractalfract8060345
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196880081&doi=10.3390%2ffractalfract8060345&partnerID=40&md5=43d131148d975d3f1e1c3b7b05962424
description This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order (Formula presented.) approaches 1, in addition to the fractional integrals we examined. © 2024 by the authors.
publisher Multidisciplinary Digital Publishing Institute (MDPI)
issn 25043110
language English
format Article
accesstype All Open Access; Gold Open Access
record_format scopus
collection Scopus
_version_ 1809678006275276800

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