Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals

Ziyi Zhou and Tingsong Du

Chaos, Solitons & Fractals, 2024, vol. 189, issue P2

Abstract: The present article is intended to address the properties and associated inequalities of multiplicative Hadamard k-fractional integrals. The core concept lies in introducing the multiplicative Hadamard k-fractional integrals. In this framework, various analytical characteristics they possess, such as ∗integrability, continuity, commutativity, semigroup property, boundedness, and others, are examined herein. Subsequently, the Hermite–Hadamard-analogous inequalities are formulated for the novelly constructed operators. Meanwhile, an identity is inferred within multiplicative Hadamard k-fractional integrals, based on which a series of Bullen-type inequalities are derived in this article, where the function Λ∗ is GG-convex and the function (lnΛ∗)s is GA-convex for s>1, with a particular focus on discussing the case when 0Keywords: Fractional multiplicative calculus; Hermite–Hadamard’s inequality; Bullen-type inequalities (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012670

DOI: 10.1016/j.chaos.2024.115715

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