Refinements of two fractional versions of Hadamard inequalities for Caputo fractional derivatives and related results

Published on Jan 9, 2021in Journal of Mass Spectrometry1.982
Ā· DOI :10.30538/OMS2021.0139
Atiqur Rehman12
Estimated H-index: 12
,
Sidra Bibi2
Estimated H-index: 2
,
Yu-Ming Chu28
Estimated H-index: 28
Source
Abstract
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Cited By10
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#1Chahn Yong Jung (Gyeongsang National University)H-Index: 7
#2Ghulam Farid (CUI: COMSATS Institute of Information Technology)H-Index: 19
Last. Josip PečarićH-Index: 36
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This article investigates new inequalities for generalized Riemannā€“Liouville fractional integrals via the refined null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null n...
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#1HĆ¼seyin Budak (DĆ¼zce University)H-Index: 15
#2Fatih Hezenci (DĆ¼zce University)H-Index: 2
Last. Hasan Kara (DĆ¼zce University)H-Index: 3
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In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null nu...
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#1Shasha Li (Harbin University of Science and Technology)
#2Ghulam Farid (CUI: COMSATS Institute of Information Technology)H-Index: 19
Last. Hafsa Yasmeen (CUI: COMSATS Institute of Information Technology)H-Index: 2
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In this article, we prove some fractional versions of Hadamard-type inequalities for strongly exponentially null null null null null null null null null null null null null null null null null null null null null null null null null null null null null - null convex functions via generalized Riemannā€“Liouville fractional integrals. The outcomes of this paper provide inequalities of strongly convex, strongly null null null null null null - convex, strongly null null null null null null - convex, s...
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#1Yan Zhao (Xinxiang Medical University)
#2M. Shoaib Saleem (University of Okara)
Last. Zabidin Salleh (UMT: Universiti Malaysia Terengganu)H-Index: 11
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Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of null null null null null null - exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomple...
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#1Xue FengH-Index: 1
#2Baolin FengH-Index: 1
Last. Ze WuH-Index: 1
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In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and strongly - convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities for - convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature.
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The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputoā€“Fabrizio fractional integral operator. In this paper, we present Hermiteā€“Hadamard-type inequalities for strongly convex functions via the Caputoā€“Fabrizio fractional integral operator. Some new inequalities of strongly c...
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#2Muhammad Shoaib Saleem (University of Okara)H-Index: 6
Last. Rahat Bano (University of Okara)
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Convexity plays an important role in many areas of mathematics, especially in the study of optimization problems where they are distinguished by a number of convenient properties. Our aim is to introduce a more extended version of convexity. In this paper, we introduced interval-valued generalized convex function and proved Hermiteā€“Hadamard-, Jensen-, and Ostrowski-type inequalities in this generalization. The presented results are generalizations of many existing results of literature.
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