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    Generalized AB-Fractional Operator Inclusions of Hermite-Hadamard's Type via Fractional Integration
    (Mdpi, 2023) Bin-Mohsin, Bandar; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Khan, Awais Gul; Budak, Huseyin; Mihai, Marcela V.; Noor, Muhammad Aslam
    The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function E-mu,alpha,l(gamma,delta, k,c) (tau; p) as a kernel in the interval domain. Additionally, a new form of Atangana-Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in E-mu,alpha,l(gamma,delta, k,c)(tau; p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.
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    Inclusions Involving Interval-Valued Harmonically Co-Ordinated Convex Functions and Raina's Fractional Double Integrals
    (Hindawi Ltd, 2022) Bin Mohsin, Bandar; Awan, Muhammad Uzair; Javed, Muhammad Zakria; Budak, Hüseyin; Khan, Awais Gul; Noor, Muhammad Aslam
    The aim of this article is to obtain some new integral inclusions essentially using the interval-valued harmonically co-ordinated convex functions and kappa-Raina's fractional double integrals. To show the validity of our theoretical results, we also give some numerical examples.
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    Jensen-Mercer Type Inequalities in the Setting of Fractional Calculus with Applications
    (Mdpi, 2022) Bin Mohsin, Bandar; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Mihai, Marcela, V; Budak, Hüseyin; Khan, Awais Gul; Noor, Muhammad Aslam
    The main objective of this paper is to establish some new variants of the Jensen-Mercer inequality via harmonically strongly convex function. We also propose some new fractional analogues of Hermite-Hadamard-Jensen-Mercer-like inequalities using AB fractional integrals. In order to obtain some of our main results, we also derive new fractional integral identities. To demonstrate the significance of our main results, we present some interesting applications to special means and to error bounds as well.
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    Unified inequalities of the q-Trapezium-Jensen-Mercer type that incorporate majorization theory with applications
    (Amer Inst Mathematical Sciences-Aims, 2023) Bin-Mohsin, Bandar; Javed, Muhammad Zakria; Awan, Muhammad Uzair; Budak, Huseyin; Khan, Awais Gul; Cesarano, Clemente; Noor, Muhammad Aslam
    The objective of this paper is to explore novel unified continuous and discrete versions of the Trapezium-Jensen-Mercer (TJM) inequality, incorporating the concept of convex mapping within the framework of q-calculus, and utilizing majorized tuples as a tool. To accomplish this goal, we establish two fundamental lemmas that utilize the & sigma;1q and & sigma;2 q differentiability of mappings, which are critical in obtaining new left and right side estimations of the midpoint q-TJM inequality in conjunction with convex mappings. Our findings are significant in a way that they unify and improve upon existing results. We provide evidence of the validity and comprehensibility of our outcomes by presenting various applications to means, numerical examples, and graphical illustrations.