EXTENSIONS OF FRACTIONAL INTEGRAL INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS

초록

The paper introduces new generalizations of well-known inequalities for convex functions using the Katugampola fractional integral, a powerful extension of the Rie-mann–Liouville fractional integral. Based on basic inequalities, we establish new estimates within the context of Katugampola fractional operators. The results are proven for convex and symmetric convex functions, with proofs that make use of integral representations, kernel properties, and estimations based on convexity. In addition, we have improved estimates for differentiable functions with convex-in-modulus derivatives. These findings offer a unifying and broad framework for fractional integral inequalities, complementing the current literature and paving the way for potential applications in fractional differential equations and functional analysis.

키워드