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    A Fractional Version of Corrected Dual-Simpson's Type Inequality via s-convex Function with Applications
    (Univ Putra Malaysia Press, 2025) Munir, A.; Qayyum, A.; Budak, H.; Qaisar, S.; Ali, U.; Supadi, S. S.
    Convexity plays a crucial role in mathematical analysis, offering profound insights into the behavior of functions and geometric shapes. Fractional integral operators generalize the classical concept of integration to non-integer orders. In this paper, we establish a new identity by using the Caputo-Fabrizio fractional integral operator. Then by using this new identity, we obtain the corrected dual Simpson's type inequalities for s-convex functions. By employing the wellknown integral inequalities such as the H & ouml;lder's inequality and power-mean inequality, we obtain new error estimates. Furthermore, we discuss the applications to some special means and quadrature formula.
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    A study of improved error bounds for Simpson type inequality via fractional integral operator
    (University of Nis, 2024) Munir, A.; Qayyum, A.; Supadi, S.S.; Budak, Hüseyin; Faiz, I.
    Fractional integral operators have been studied extensively in the last few decades, and many different types of fractional integral operators have been introduced by various mathematicians. In 1967 Michele Caputo introduced Caputo fractional derivatives, which defined one of these fractional operators, the Caputo Fabrizio fractional integral operator. The main aim of this article is to established the new integral equalities related to Caputo-Fabrizio fractional integral operator. By incorporating this identity and convexity theory to obtained a novel class of Simpson type inequality. In this paper, we present a novel generalization of Simpson type inequality via s-convex and quasi-convex functions. Then, utilizing this identity the bounds of classical Simpson type inequality is improved. Finally, we discussed some applications to Simpson's quadrature rule. © 2024, University of Nis. All rights reserved.