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

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  • Zhang, Xiaohua
  • Peng, Yu
  • Du, Tingsong

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.

Suggested Citation

  • Zhang, Xiaohua & Peng, Yu & Du, Tingsong, 2025. "(k,s)-fractional integral operators in multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:chsofr:v:195:y:2025:i:c:s0960077925003169
    DOI: 10.1016/j.chaos.2025.116303
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    References listed on IDEAS

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    1. Zhou, Ziyi & Du, Tingsong, 2024. "Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    2. Wang, Mei-Chih & Chang, Tsangyao & Mikhaylov, Alexey & Linyu, Jia, 2024. "A measure of quantile-on-quantile connectedness for the US treasury yield curve spread, the US Dollar, and gold price," The North American Journal of Economics and Finance, Elsevier, vol. 74(C).
    3. Dawood Khan & Saad Ihsan Butt & Youngsoo Seol, 2025. "ANALYSIS ON MULTIPLICATIVELY (P,m)-SUPERQUADRATIC FUNCTIONS AND RELATED FRACTIONAL INEQUALITIES WITH APPLICATIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-27.
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    5. Arslan Munir & Miguel Vivas-Cortez & Ather Qayyum & Hüseyin Budak & Irza Faiz & Siti Suzlin Supadi, 2024. "Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 30(1), pages 543-566, December.
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    7. Tingsong Du & Chunyan Luo & Zhijie Cao, 2021. "On The Bullen-Type Inequalities Via Generalized Fractional Integrals And Their Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-20, November.
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    1. Du, Tingsong & Zhou, Ziyi & Tan, Zongrui, 2025. "Hadamard functional integral operators within fractional multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).

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