Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions

Abstract

This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.

Keywords

• fractional integrals
• milne-type inequalities
• functions of bounded variation
• convex functions
• bounded functions