Study of fractional integral inequalities involving Mittag-Leffler functions via convexity

Abstract

Abstract This paper studies fractional integral inequalities for fractional integral operators containing extended Mittag-Leffler (ML) functions. These inequalities provide upper bounds of left- and right-sided fractional integrals for ( α , h − m ) $(\alpha, h-m)$ convex functions. A generalized fractional Hadamard inequality is established. All the results hold for h-convex, ( h , m ) $(h, m)$ -convex, ( α , m ) $(\alpha, m)$ -convex, ( s , m ) $(s, m)$ -convex, and associated functions.

Keywords

• Convex function
• ( α , h − m ) $(\alpha,h-m)$ -convex function
• Mittag-Leffler function
• Fractional integral operators