(k,s)-fractional integral operators in multiplicative calculus

Xiaohua Zhang, Yu Peng and Tingsong Du

Chaos, Solitons & Fractals, 2025, vol. 195, issue C

Abstract: The research here endeavors to delve into the trapezoid-type inequalities pertaining to multiplicative (k,s)-fractional integrals. To this end, we introduce a class of operators, called the multiplicative (k,s)-fractional integrals, and subsequently give an analysis of these newly minted operators, examining their characteristics including boundedness, continuity, commutative properties, semigroup property, and several others. Moreover, leveraging the fractional integral identity, we derive three trapezoid-type inequalities of multiplicative type, where the function U∗ possesses multiplicative convexity or (lnU∗)q maintains convexity for q>1.

Keywords: Hermite–Hadamard’s inequality; Multiplicative Riemann–Liouville fractional integrals; Multiplicative calculus (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:195:y:2025:i:c:s0960077925003169

DOI: 10.1016/j.chaos.2025.116303

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