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Fractional Julia sets on time scales

Author

Listed:
  • Wang, Yupin
  • Wei, Tengda
  • Du, Feifei
  • Li, Hui
  • Liu, Shutang

Abstract

In this paper, fractional Julia sets are constructed through fractional difference equations defined on time scale T(q,h). The influence of memory and scale within the fractional (q, h)-difference system on its fractal dynamics is elucidated through an exploration of how memory, geometric, and algebraic parameters shape the resulting Julia sets. Numerical investigations using box-counting dimension analysis and symmetry criteria uncover intricate properties of these sets, such as their resilience to perturbations, while their central symmetry in a particular scenario is established.

Suggested Citation

  • Wang, Yupin & Wei, Tengda & Du, Feifei & Li, Hui & Liu, Shutang, 2026. "Fractional Julia sets on time scales," Applied Mathematics and Computation, Elsevier, vol. 514(C).
    • Handle: RePEc:eee:apmaco:v:514:y:2026:i:c:s0096300325005727
    DOI: 10.1016/j.amc.2025.129847
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    References listed on IDEAS

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    1. Wang, Yupin & Li, Xiaodi & Wang, Da & Liu, Shutang, 2022. "A brief note on fractal dynamics of fractional Mandelbrot sets," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Wang, Yupin, 2023. "Fractional quantum Julia set," Applied Mathematics and Computation, Elsevier, vol. 453(C).
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