Korean J. Math. Vol. 31 No. 1 (2023) pp.75-94
DOI: https://doi.org/10.11568/kjm.2023.31.1.75

Fractional versions of Hadamard inequalities for strongly $(s,m)$-convex functions via Caputo fractional derivatives

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Published: Mar 30, 2023
Keywords:
Convex function, Strongly convex function, Hadamard inequality, Caputo fractional derivatives
Mathematics Subject Classification:
33E12, 26A51, 26A33

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Ghulam Farid
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan.
Sidra Bibi
Govt. Girls Primary School, Kamra Khurd, Attock 43570, Pakistan.
Laxmi Rathour
Ward number: 16, Bhagatbandh, Anuppur 484 224, Madhya Pradesh, India.
Lakshmi Narayan Mishra
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632 014, India
Vishnu Narayan Mishra
Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak 484 887, Anuppur, Madhya Pradesh, India

Abstract

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly $(s,m)$-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.



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