Hadamard functional integral operators within fractional multiplicative calculus

Tingsong Du, Ziyi Zhou and Zongrui Tan

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

Abstract: This research focuses on analyzing multiplicative Hadamard functional fractional integral operators and applies them to establish Bullen-type inequalities for twice ∗differentiable functions. The investigation begins with the formalization of Hadamard functional integrals in fractional multiplicative calculus, followed by an analysis of their fundamental properties, including continuity, boundedness, ∗integrability, ∗linearity, and others. Based on the introduced operators again, we derive a fractional integral identity to establish bounds for Bullen-type inequalities. Our results hold under the assumptions that either (i) the second multiplicative derivative P∗∗ is multiplicatively convex, or (ii) (lnP∗∗)q1 is convex for q1>1. Additionally, we provide insights into the case 0Keywords: Twice *differentiable functions; Multiplicative Hadamard functional fractional integrals; Multiplicatively convex functions; Bullen-type inequalities (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007234

DOI: 10.1016/j.chaos.2025.116710

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