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    The Multi-Parameter Fractal-Fractional Inequalities For Fractal (P,M)-Convex Functions
    (World Scientific Publ Co Pte Ltd, 2024) Yuan, Xiaoman; Budak, Hueseyin; Du, Tingsong
    Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal-fractional integral inequalities containing the fractal (P,m)-convex functions. Initially, we formulate the new conception of the fractal (P,m)-convex functions and work on a variety of properties. Through the assistance of the fractal-fractional integrals, the 2l-fractal identity with multiple parameters is established, and from that, integral inequalities are inferred regarding twice fractal differentiable functions which are fractal (P,m)-convex. Furthermore, a few typical and novel outcomes are discussed and visualized for specific parameter values, separately. It concludes with some applications in respect of the special means, the quadrature formulas and random variable moments, respectively.
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    Newton-type Inequalities for Fractional Integrals by Various Function Classes
    (Emrah Evren KARA, 2025) Hezenci, Fatih; Budak, H¨Useyin; Du, Tingsong
    The authors of the paper examine some Newton-type inequalities for various function classes using Riemann-Liouville fractional integrals. Namely, we establish some Newton-type inequalities for bounded functions by fractional integrals. In addition, we construct some fractional Newton-type inequalities for Lipschitzian functions. Furthermore, we offer some Newton-type inequalities by fractional integrals of bounded variation. Finally, we provide our results by using special cases of theorems and obtained examples. © 2025 Elsevier B.V., All rights reserved.