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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.