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    A New extension of Hermite Hadamard inequalities associating ψ-Hilfer fractional integral
    (Palestine Polytechnic University, 2025) Qayyum, Ather; Budak, H¨Useyin; Bat, Umut; Kara, Hasan; Munir, Arslan; Rathour, Laxmi
    Fractional inequalities have been an essential topic in mathematics and have found applications in various domains. In this article, we established some new bounds (below and above) for mid-point type inequality and trapezoidal-type inequality for ψ-Hilfer- fractional integral by utilizing functions whose second derivatives are bounded. We also investigate some new generalization and extension of Hermite-Hadamard type inequalities for ψ-Hilfer fractional integrals for the functions having the condition: (Formula presented). © 2025 Elsevier B.V., All rights reserved.
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    A NOTE ON SIMPSON 3/8 RULE FOR FUNCTION WHOSE MODULUS OF FIRST DERIVATIVES ARE s-CONVEX FUNCTION WITH APPLICATION
    (Kangwon-Kyungki Mathematical Soc, 2024) Munir, Arslan; Budak, Huseyin; Kara, Hasan; Rathour, Laxmi; Faiz, Irza
    Researchers continue to explore and introduce new operators, methods, and applications related to fractional integrals and inequalities. In recent years, fractional integrals and inequalities have gained a lot of attention. In this paper, firstly we established the new identity for the case of differentiable function through the fractional operator (Caputo-Fabrizio). By utilizing this novel identity, the obtained results are improved for Simpson second formula-type inequality. Based on this identity the Simpson second formula-type inequality is proved for the s-convex functions. Furthermore, we also include the applications to special means.