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    Generalizations of Simpson type inequality for (?, m)-convex functions
    (Univ Nis, Fac Sci Math, 2024) Munir, Arslan; Budak, Huseyin; Faiz, Irza; Qaisar, Shahid
    Several scholars are interested in fractional operators with integral inequalities. Due to its characteristics and wide range of applications in science, engineering fields, artificial intelligence and fractional inequalities should be employed in mathematical investigations. In this paper, we establish the new identity for the Caputo-Fabrizio fractional integral operator. By utilizing this identity, the generalization of Simpson type inequality for ( alpha, m ) -convex functions via the Caputo-Fabrizio fractional integral operator. Furthermore, we also include the applications to special means, q -digamma functions, Simpson formula, Matrix inequalities, Modified Bessel function, and mind -point formula. These applications have given a new dimension to scholars.
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    Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function
    (Taylor & Francis Inc, 2024) Munir, Arslan; Vivas-Cortez, Miguel; Qayyum, Ather; Budak, Huseyin; Faiz, Irza; Supadi, Siti Suzlin
    Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for $s$s-convex function are obtained. By employing well-known inequalities such as H & ouml;lder's and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.