REMARKS ON INEQUALITIES WITH PARAMETER BY CONFORMABLE FRACTIONAL INTEGRALS

Fatih Hezenci (), Miguel Vivas-Cortez and HÃœSEYIN Budak ()
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Fatih Hezenci: Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkey
Miguel Vivas-Cortez: ��Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Católica del Ecuador, Sede Quito, Ecuador
HÃœSEYIN Budak: Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkey

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-16

Abstract: We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established by using the conformable fractional integrals. Namely, we show that our main inequalities reduce to Ostrowski-, Hermite–Hadamard-, Simpson-, and Bullen-type inequalities which are proved in earlier published papers. More precisely, some inequalities are acquired by taking advantage of the convexity, the Hölder, and the power mean inequalities. Finally, examples are given to illustrate the investigated results.

Keywords: Ostrowski-Type Inequality; Hermite–Hadamard-Type Inequality; Simpson-Type Inequality; Bullen-Type Inequality; Fractional Conformable Integrals; Fractional Calculus; Convex Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501378

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