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Hadamard functional integral operators within fractional multiplicative calculus

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  • Du, Tingsong
  • Zhou, Ziyi
  • Tan, Zongrui

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 0

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  • Du, Tingsong & Zhou, Ziyi & Tan, Zongrui, 2025. "Hadamard functional integral operators within fractional multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007234
    DOI: 10.1016/j.chaos.2025.116710
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