IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v199y2025ip2s0960077925007234.html

Hadamard functional integral operators within fractional multiplicative calculus

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925007234
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116710?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Yun Long & Tingsong Du, 2025. "ANALYSIS ON MULTIPLICATIVE k-ATANGANA–BALEANU FRACTIONAL INTEGRALS WITH APPLICATION TO VARIOUS MERCER-TYPE INEQUALITIES," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-37.
    2. Zhou, Ziyi & Du, Tingsong, 2024. "Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    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.
    4. Zongrui Tan & Tingsong Du, 2025. "ANALYTICAL PROPERTIES ON MULTIPLICATIVELY MψA-p-FUNCTIONS AND RELATED MULTIPLICATIVE ψ-HILFER FRACTIONAL TRAPEZOID-TYPE INEQUALITIES," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(07), pages 1-27.
    5. Muhammad Umar & Saad Ihsan Butt & Youngsoo Seol, 2025. "Hybrid Fractional Integral Inequalities In Multiplicative Calculus With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-28.
    6. Saad Ihsan Butt & Muhammad Umar & Dawood Khan & Youngsoo Seol, 2025. "Fractional Version Of Bullen-Type Inequalities Via Multiplicative Calculus With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(09), pages 1-23.
    7. Zhang, Xiaohua & Peng, Yu & Du, Tingsong, 2025. "(k,s)-fractional integral operators in multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    8. Muhammad Amer Latif, 2024. "Refinements and Applications of Hermite–Hadamard-Type Inequalities Using Hadamard Fractional Integral Operators and GA -Convexity," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    9. Dafang Zhao & Muhammad Aamir Ali & Hãœseyin Budak & Zai-Yin He, 2023. "Some Bullen-Type Inequalities For Generalized Fractional Integrals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-11.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Xiaohua & Peng, Yu & Du, Tingsong, 2025. "(k,s)-fractional integral operators in multiplicative calculus," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    2. Wedad Saleh & Badreddine Meftah & Muhammad Uzair Awan & Abdelghani Lakhdari, 2025. "On Katugampola Fractional Multiplicative Hermite-Hadamard-Type Inequalities," Mathematics, MDPI, vol. 13(10), pages 1-34, May.
    3. Bas, Umut & Akkurt, Abdullah & Has, Aykut & Yildirim, Huseyin, 2025. "Multiplicative Riemann–Liouville fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    4. Zhou, Ziyi & Du, Tingsong, 2024. "Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    5. Demir, İzzettin & Üneş, Esra, 2025. "Fractional integral approaches to weighted corrected Euler–Maclaurin-type inequalities for different classes of functions," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007234. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.