New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

Abstract

In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions

“…Sitthiwirattham et al [17] have discovered some estimates for Simpson's 3/8 formula using the Riemann-Liouville fractional integrals operators. For other inequalities involving fractional integral operators, see [1,6,16,19] and the references therein.…”

Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions

“…Numerous fractional-order research findings on the HH-inequality have recently been published. Examples include the Riemann-Liouville fractional integral inequalities [15][16][17][18][19][20][21][22][23][24], conformable fractional integral inequalities [25], k-Riemann-Liouville fractional integral inequalities [26], and local fractional integral inequalities [27][28][29][30][31][32][33][34][35][36][37][38][39].…”