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    Advancements in corrected Euler-Maclaurin-type inequalities via conformable fractional integrals
    (Springer, 2025) Acar, Yaren; Budak, Huseyin; Bas, Umut; Hezenci, Fatih; Yildirim, Huseyin
    In this research article, equality is proved to obtain corrected Euler-Maclaurin-type inequalities. Using this identity, we establish several corrected Euler-Maclaurin-type inequalities for the case of differentiable convex functions by means of conformable fractional integrals. Moreover, some corrected Euler-Maclaurin-type inequalities are given for bounded functions by fractional integrals. Additionally, fractional corrected Euler-Maclaurin-type inequalities are constructed for Lipschitzian functions. Finally, corrected Euler-Maclaurin-type inequalities are considered by fractional integrals of bounded variation.
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    NEW EXTENSIONS OF THE HERMITE-HADAMARD INEQUALITIES BASED ON ψ-HILFER FRACTIONAL INTEGRALS
    (Korean Soc Mathematical Education, 2024) Budak, Huseyin; Bas, Umut; Kara, Hasan; Samei, Mohammad Esmael
    This article presents the above and below bounds for Midpoint and Trapezoid types inequalities for 95-Hilfer fractional integrals with the assistance of the functions whose second derivatives are bounded. We also possess some extensions and generalizations of Hermite-Hadamard inequalities via 95-Hilfer fractional integrals with the aid of the functions that have the conditions that will said.
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    NEW EXTENSIONS VERSION OF HERMITE-HADAMARD TYPE INEQUALITIES BY MEANS OF CONFORMABLE FRACTIONAL INTEGRALS
    (Univ Miskolc Inst Math, 2024) Bas, Umut; Budak, Huseyin; Kara, Hasan
    In the current investigation, we acquire the upper and lower bounds for inequalities of midpoint-type and trapezoid-type involving conformable fractional integral operators with the help of the mappings whose second derivatives are bounded. We support the established inequalities with examples. Moreover, we use graphs to demonstrate the correctness of the given examples. What's more, we prove the Hermite-Hadamard inequality, which includes conformable fractional integrals, with the aid of condition f ' (a + b t) f ' (t) >= 0, t is an element of a, a+b than the convexity of function.
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    New trapezoid type inequalities for differentiable functions
    (Univ Nis, 2023) Yavuz, Melike; Budak, Hüseyin; Bas, Umut
    In this paper, we first establish that an identity involving generalized fractional integrals for twice differentiable functions. By using this equality, we obtain some trapezoid type inequalities for the functions whose second derivatives in absolute value are convex.
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    Novel results of Milne-type inequalities involving tempered fractional integrals
    (Springer, 2024) Hezenci, Fatih; Budak, Hüseyin; Kara, Hasan; Bas, Umut
    In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of our study. This identity paves the way for the Milne-type inequalities, which are explored through the framework of differentiable convex mappings inclusive of tempered fractional integrals. The significance of these mappings in the realm of fractional calculus is underscored by their ability to extend classical concepts into more complex, fractional dimensions. In addition, by using the Holder inequality and power-mean inequality, we acquire some new Milne-type inequalities. Moreover, the practicality and theoretical relevance of our findings are further demonstrated through the application of specific cases derived from the theorems.
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    SOME BOUNDS OF HERMITE-HADAMARD-TYPE INEQUALITIES BASED ON CONFORMABLE FRACTIONAL INTEGRALS
    (Univ Miskolc Inst Math, 2025) Budak, Huseyin; Bas, Umut; Kara, Hasan; Hezenci, Fatih
    In this research, we establish the above and below bounds via the left and right sides of Hermite-Hadamard-type inequalities including conformable fractional integrals with the aid of the mappings whose second derivatives are bounded. Instead of using the convexity condition [] in these obtained inequalities, we used condition f ' (a + b-t)-f ' (t) >= 0, t E a, a+b 2 . We have presented examples of the inequalities acquired. We have given the graph showing the correctness of the presented examples.