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

Abstract

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.

Keywords

• Trapezium inequality
• Harmonic convex function
• Riemann–Liouville fractional integrals
• Hölder inequality
• Power mean inequality
• Special means