Fractal analysis of financial markets using Laplace–Mittag-Leffler distributions

Zahra Alizade, Hamzeh Agahi and Somayeh Khademloo

Chaos, Solitons & Fractals, 2025, vol. 199, issue P3

Abstract: The article presents advancements in financial mathematics through its integration of Laplace–Mittag-Leffler distributions with fractal geometry. By establishing direct mathematical relationships between distribution parameters and market complexity metrics, the authors provide a robust framework for analyzing extreme price movements. This approach resolves longstanding limitations of traditional models through its inherent capacity to capture heavy-tailed distributions and persistent memory effects, offering superior predictive accuracy during market turbulence. The methodology’s foundation in fractional calculus enables precise modeling of scale-invariant patterns observed in real-world financial data, creating essential bridges between theoretical mathematics and practical market analysis.

Keywords: Fractal finance; Mittag-Leffler distribution; Market turbulence; Non-equilibrium dynamics; Scaling laws; Nonlinear dynamics (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925008604

DOI: 10.1016/j.chaos.2025.116847

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