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Multiplicative Riemann–Liouville fractional integrals and derivatives

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  • Bas, Umut
  • Akkurt, Abdullah
  • Has, Aykut
  • Yildirim, Huseyin

Abstract

This study explores the connections between fractional calculus, a field that has recently garnered significant research interest, and multiplicative analysis. The introduction provides a comprehensive overview of the historical development and foundational concepts of these areas. The preliminary section outlines key definitions and illustrative examples from multiplicative analysis. The research derives the multiplicative representations of the gamma and beta functions and examines their fundamental properties. Furthermore, generalizations of integrals and derivatives within the framework of multiplicative analysis are formulated, accompanied by explicit formulas for multiplicative integrals and derivatives. Finally, fractional-order multiplicative integral derivatives for selected functions are introduced and visualized through graphical representations, highlighting their practical implications.

Suggested Citation

  • Bas, Umut & Akkurt, Abdullah & Has, Aykut & Yildirim, Huseyin, 2025. "Multiplicative Riemann–Liouville fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925003236
    DOI: 10.1016/j.chaos.2025.116310
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    References listed on IDEAS

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    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. Mehmet Zeki Sarikaya & Hasan Ogunmez, 2012. "On New Inequalities via Riemann‐Liouville Fractional Integration," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. An, Jaehyung & Mikhaylov, Alexey & Chang, Tsangyao, 2024. "Relationship between the popularity of a platform and the price of NFT assets," Finance Research Letters, Elsevier, vol. 61(C).
    5. Mehmet Zeki Sarikaya & Hasan Ogunmez, 2012. "On New Inequalities via Riemann-Liouville Fractional Integration," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, October.
    6. Hasan Kara & Hüseyin Budak & Fatih Hezenci, 2022. "New Extensions of the Parameterized Inequalities Based on Riemann–Liouville Fractional Integrals," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    7. Dinçer, Hasan & Yüksel, Serhat & An, Jaehyung & Mikhaylov, Alexey, 2024. "Quantum and AI-based uncertainties for impact-relation map of multidimensional NFT investment decisions," Finance Research Letters, Elsevier, vol. 66(C).
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