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Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional (p , q) -calculus on finite intervals, particularly the fractional (p , q) -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional (p , q) -integral on finite intervals. Then, the obtained results are used to derive some fractional (p , q) -trapezoid and (p , q) -midpoint type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities. [ABSTRACT FROM AUTHOR]

In this paper we establish some related Ostrowski inequalities for the case of convex functions and general Lebesgue integral on measurable spaces. Midpoint and integral mean inequalities are provided, some particular results related to the famous Fejér's inequality are also given. [ABSTRACT FROM AUTHOR]

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequality for convex functions is obtained by using only the right Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize the studies [1, 4, 6]. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, a similar equality which is given in [Ç. Yıldız, M. E. Özdemir, M. Z. Sarıkaya, Kyungpook Math. J., 56 (2016), 161-172] is proved by using different symbols and impressions. By using this equality, some new fractional integral inequalities for s-convex functions are obtained. Also, some applications to special means of positive real numbers are given. If the α = 1 is taken, our results coincide with the results given in [E. Set, M. E. Özdemir, M. Z. Sarıkaya, Facta Unv. Ser. Math. Inform., 27 (2012), 67-82] so our results are more general from the results given there. [ABSTRACT FROM AUTHOR]

Recently, in [5], with a new approach, the authors obtained a new fractional Hermite-Hadamard type inequality for convex functions by using only the left Riemann-Liouville fractional integral. They also had new equalities to have new fractional trapezoid and midpoint type inequalities for convex functions, In this papers, we will use the same equalities to have new fractional trapezoid and midpoint type inequalities for quasi-convex functions. Our results generalise the study [3]. [ABSTRACT FROM AUTHOR]

In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejér inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard- Fejer inequality and better than given in [9] by Sarıkaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kırmacı. [ABSTRACT FROM AUTHOR]

Abstract Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q-trapezoid and q-midpoint type inequalities. Fractional ( p , q ) $(p,q)$ -calculus on finite intervals, particularly the fractional ( p , q ) $(p,q)$ -integral inequalities, has been studied. In this paper, we study two identities for continuous functions in the form of fractional ( p , q ) $(p,q)$ -integral on finite intervals. Then, the obtained results are used to derive some fractional ( p , q ) $(p,q)$ -trapezoid and ( p , q ) $(p,q)$ -midpoint type inequalities.

In this work, we pose a new equality for differentiable functions. By using this equality, we have some new Ostrowki type inequalities and some error estimates for the midpoint formula for functions whose derivatives in absolute values at certain powers are harmonically convex. [ABSTRACT FROM AUTHOR]

In this work, we reveal a new equality for differentiable functions. By using this equality, we have some new Ostrowki type inequalities and some error estimates for the midpoint formula for functions whose derivatives in absolute values at certain powers are GA-convex. [ABSTRACT FROM AUTHOR]