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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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    New results on Hermite–Hadamard type inequalities via Caputo-Fabrizio fractional integral for s-convex function
    (University of Nis, 2023) Nasir, J.; Qaisar, S.; Qayyum, A.; Budak, Hüseyin
    The purposeiof thisiarticle is to construction Hermite–Hadamard itype inequalities viaiCaputo-Fabrizio fractional integralifor s-convexifunction. The results are applied to fractionalivariations of Hermite– Hadamarditype inequalities foridifferentiableimapping ? with s-convexiabsolute value derivatives. The findings also provide a new lemma for ?? and new limitsivia Caputo-Fabrizio fractionalioperator by using the well-knowniHölder’s integral inequalities. Moreover some new boundsifor applications of matrix and special means of different positive real numbers are also discussed. © 2023, University of Nis. All rights reserved.