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

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  • Alizade, Zahra
  • Agahi, Hamzeh
  • Khademloo, Somayeh

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.

Suggested Citation

  • Alizade, Zahra & Agahi, Hamzeh & Khademloo, Somayeh, 2025. "Fractal analysis of financial markets using Laplace–Mittag-Leffler distributions," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925008604
    DOI: 10.1016/j.chaos.2025.116847
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    References listed on IDEAS

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    Cited by:

    1. Stanis{l}aw M. S. Halkiewicz, 2025. "The Omniscient, yet Lazy, Investor," Papers 2510.24467, arXiv.org.

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