Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

Abstract

In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.

A study on Hermite-Hadamard type inequalities for s-convex functions via conformable fractional integrals

“…Now, lets us give some necessary definition and mathematical preliminaries of fractional calculus theory as follows, which are used lots of study. For more details, one can consult ( [8]- [10], [14], [16]- [23], [28]). …”

New Generalized Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

“…Using the above approach, many new inequalities have been obtained and reported in the literature. For example, an important theorem was established through the Riemann-Liouville fractional calculus and reported in [19] as follows.…”

“…In order to improve the identity established in [19] for generalized fractional integrals, the following lemma can be used to prove our results.…”

Refinements and similar extensions of Hermite–Hadamard inequality for fractional integrals and their applications

“…R, is known in the literature as Hermite-Hadamard inequality [7]. For some results which generalize, improve, and extend the inequality (1.1), refer to [1][2][3][4][5][6][8][9][10][11][12][13][14][15][16][17][18].…”