Some new approaches of integral inequalities involving Raina and Mittag-Leffler function pertaining to Atangana-Baleanu fractional integral operator

Volume 41, Issue 2, pp 244--263 https://dx.doi.org/10.22436/jmcs.041.02.07

Publication Date: October 17, 2025 Submission Date: June 02, 2025 Revision Date: July 20, 2025 Accteptance Date: August 30, 2025

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Authors

M. Tariq - Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey. - Department of Mathematics, Balochistan Residential College, Loralai, Balochistan, Loralai, Balochistan, Pakistan. S. K. Ntouyas - Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece. W. Afzal - Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan. J. Tariboon - Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

Abstract

Convexity and inequality, particularly as they relate to fractional analysis, have a plethora of significant applications in the applied sciences. Our goal in this manuscript is to investigate and develop a new version of the Hermite-Hadamard and Pachpatte types of integral inequality using the Atangana-Baleanu fractional integral operator in the context of generalized convex involving Raina's function. Utilizing this method, we develop a new identity for fractional integrals that is associated with Raina's functions. Additionally, some new extensions of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator are examined with the support of Hölder inequality, power mean inequality and Young inequaity. Additionally, we present applications related to entropy measures that demonstrate the practical utility of our main findings. In terms of both outcomes and special cases, this study presents novel and noteworthy improvements over previously published findings.

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Keywords

• Convex function
• Raina function
• generalized convex involving Raina's function
• AB fractional operator

MSC

•  26A51
•  26A33
•  26D07
•  26D10
•  26D15

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