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The aim of this research article is to use the extended fractional operators involving the multivariate Mittag–Leffler (M-M-L) function, we provide the generalization of the Hermite–Hadamard–Fejer (H-H-F) inequalities. We relate these inequalities to previously published disparities in the literature by making appropriate substitutions. In the last section, we analyze several inequalities related to the H-H-F inequalities, focusing on generalized h-convexity associated with extended fractional operators involving the M-M-L function. To achieve this, we derive two identities for locally differentiable functions, which allows us to provide specific estimates for the differences between the left, middle, and right terms in the H-H-F inequalities. Also, we have constructed specific inequalities and visualized them through graphical representations to facilitate their applications in analysis. The research bridges theoretical advancements with practical applications, providing high-accuracy bounds for complex systems involving fractional calculus.
Details
; Rahman, Gauhar 3
; Haque, Salma 4 ; Aloqaily, Ahmad 4
; Mlaiki, Nabil 4
1 School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China;
2 Department of Mathematics, University of Sargodha, Sargodha P.O. Box 40100, Pakistan;
3 Department of Mathematics & Statistics, Hazara University, Mansehra 21300, Pakistan;
4 Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia;