Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities

Abstract

In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.

Keywords

• milne type inequalities
• convex function
• fractional integrals
• bounded function
• function of bounded variation