KATUGAMPOLA FRACTIONAL INTEGRAL INEQUALITIES IN MULTIPLICATIVE CALCULUS WITH MULTIPLE PARAMETERS

This work focuses on the investigation of multi-parameterized inequalities for [Formula: see text]differentiable functions through the framework of multiplicative Katugampola fractional integrals. Central to our approach is the derivation of a multi-parameterized identity associated with the multiplicative Katugampola fractional integrals, which serves as the cornerstone for constructing a family of multi-parameterized inequalities. The established results hold under convexity conditions: either multiplicative convexity of [Formula: see text] or convexity of [Formula: see text] for [Formula: see text]. To demonstrate the practical implications, we supplement the theoretical analysis with numerical examples accompanied by graphical visualizations, providing concrete verification of the proposed inequalities. Furthermore, we present applications of the obtained inequalities to quadrature formulas and special means.