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Hadamard’s inequality and its extensions for conformable fractional integrals of any order \(\alpha > 0\). (English) Zbl 1463.26069

Summary: Recently the authors T. Abdeljawad [J. Comput. Appl. Math. 279, 57–66 (2015; Zbl 1304.26004)] and R. Khalil et al. [J. Comput. Appl. Math. 264, 65–70 (2014; Zbl 1297.26013)] introduced a new and simple well-behaved concept of fractional integral called conformable fractional integral. In this article, we establish Hermite-Hadamard’s inequalities for conformable fractional integral. We also give extensions of Hermite-Hadamard type inequalities for conformable fractional integrals.

MSC:

26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals