New extensions version of Hermite–Hadamard type inequalities by means of conformable fractional integrals

Bas, Umut and Budak, Hüseyin and Kara, Hasan (2024) New extensions version of Hermite–Hadamard type inequalities by means of conformable fractional integrals. Miskolc Mathematical Notes, 25 (2). pp. 603-615. ISSN 1787-2413

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Abstract

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 ∈ [a, (a+b)/2 ] rather than the convexity of function.

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