Some New Harmonically Convex Function Type Generalized Fractional Integral Inequalities

Abstract

In this article, we established a new version of generalized fractional Hadamard and Fejér–Hadamard type integral inequalities. A fractional integral operator (FIO) with a non-singular function (multi-index Bessel function) as its kernel and monotone increasing functions is utilized to obtain the new version of such fractional inequalities. Our derived results are a generalized form of several proven inequalities already existing in the literature. The proven inequalities are useful for studying the stability and control of corresponding fractional dynamic equations.

Keywords

• bessel function
• harmonically convex function
• non-singular function involving kernel fractional operator
• harmonically convex function
• Hadamard inequality
• Fejér–Hadamard inequality