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In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann–Liouville fractional integrals and Riemann integrals. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers. [ABSTRACT FROM AUTHOR]

In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (İşcan in Hacet. J. Math. Stat. 43(6):935–942, 2014 and İşcan and Wu in Appl. Math. Comput. 238:237–244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite–Hadamard type. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some generalized fractional integral inequalities of the Hermite–Hadamard type for (α , m) -convex functions, show that one can find some Riemann–Liouville fractional integral inequalities and classical integral inequalities of the Hermite–Hadamard type, and generalize and extend some known results. [ABSTRACT FROM AUTHOR]