Extension of Milne-type inequalities to Katugampola fractional integrals

Abstract

Abstract This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.

Keywords

• Katugampola fractional integral operators
• Milne-type inequalities
• Convex functions
• P-functions
• s-Godunova-Levin functions
• Extended s-convex functions