KATUGAMPOLA FRACTIONAL INTEGRAL INEQUALITIES IN MULTIPLICATIVE CALCULUS WITH MULTIPLE PARAMETERS

Tingsong Du and Dingyi Ai ()
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Tingsong Du: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China2College of Mathematics and Physics, China Three Gorges University, Yichang 443002, P. R. China
Dingyi Ai: College of Mathematics and Physics, China Three Gorges University, Yichang 443002, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 09, 1-26

Abstract: This work focuses on the investigation of multi-parameterized inequalities for ∗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 𠒵∗ or convexity of (ln𠒵∗)q0 for q0 > 1. 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.

Keywords: Katugampola Fractional Integrals; Radau-Type Inequalities; Multiplicatively Convex Functions; Multiplicative Calculus (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500884

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