Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function

Arslan Munir, Miguel Vivas-Cortez, Ather Qayyum, Hüseyin Budak, Irza Faiz and Siti Suzlin Supadi

Mathematical and Computer Modelling of Dynamical Systems, 2024, vol. 30, issue 1, 543-566

Abstract: 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 Hölder’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.

Date: 2024
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DOI: 10.1080/13873954.2024.2356698

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