Refinements of some fractional integral inequalities for refined ( α , h − m ) $(\alpha ,h-m)$ -convex function

Abstract

Abstract This article investigates new inequalities for generalized Riemann–Liouville fractional integrals via the refined ( α , h − m ) $(\alpha ,h-m)$ -convex function. The established results give refinements of fractional integral inequalities for ( h − m ) $(h-m)$ -convex, ( α , m ) $(\alpha ,m)$ -convex, ( s , m ) $(s,m)$ -convex, and related functions. Also, the k-fractional versions of given inequalities by using a parameter substitution are provided.

Keywords

• Refined ( α , h − m ) $(\alpha ,h-m)$ -convex function
• Refined ( h − m ) $(h-m)$ -convex function
• Hermite–Hadamard inequality
• Riemann–Liouville fractional integrals