Multiplicative Riemann–Liouville fractional integrals and derivatives

Umut Bas, Abdullah Akkurt, Aykut Has and Huseyin Yildirim

Chaos, Solitons & Fractals, 2025, vol. 196, issue C

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.

Keywords: Multiplicative calculus; Non-Newtonian calculus; Fractional integrals; Fractional derivatives; Fractional calculus; Newtonian analysis (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925003236

DOI: 10.1016/j.chaos.2025.116310

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