On a Certain Class of <i>GA</i>-Convex Functions and Their Milne-Type Hadamard Fractional-Integral Inequalities

Abstract

In this article, we prove a new Milne-type inequality involving Hadamard fractional integrals for functions with GA-convex first derivatives. The limits of the error estimates involve incomplete gamma and confluent hypergeometric functions. The results of this study open the door to further investigation of this subject, as well as extensions to other forms of generalized convexity, weighted formulas, and higher dimensions.

Keywords

• Hadamard fractional integrals
• Milne-type integral inequalities
• incomplete gamma function
• <i>GA</i>-convex functions
• incomplete confluent hypergeometric function