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On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric

Author

Listed:
  • Weberszpil, J.
  • Lazo, Matheus Jatkoske
  • Helayël-Neto, J.A.

Abstract

Over the recent decades, diverse formalisms have emerged that are adopted to approach complex systems. Amongst those, we may quote the q-calculus in Tsallis’ version of Non-Extensive Statistics with its undeniable success whenever applied to a wide class of different systems; Kaniadakis’ approach, based on the compatibility between relativity and thermodynamics; Fractional Calculus (FC), that deals with the dynamics of anomalous transport and other natural phenomena, and also some local versions of FC that claim to be able to study fractal and multifractal spaces and to describe dynamics in these spaces by means of fractional differential equations.

Suggested Citation

  • Weberszpil, J. & Lazo, Matheus Jatkoske & Helayël-Neto, J.A., 2015. "On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 399-404.
    • Handle: RePEc:eee:phsmap:v:436:y:2015:i:c:p:399-404
    DOI: 10.1016/j.physa.2015.05.063
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    Citations

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    Cited by:

    1. Qiu, Lin & Lin, Ji & Chen, Wen & Wang, Fajie & Hua, Qingsong, 2020. "A novel method for image edge extraction based on the Hausdorff derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Umpierrez, Haridas & Davis, Sergio, 2021. "Fluctuation theorems in q-canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    4. Chen, Wen & Hei, Xindong & Sun, Hongguang & Hu, Dongliang, 2018. "Stretched exponential stability of nonlinear Hausdorff dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 259-264.
    5. Goulart, A.G. & Lazo, M.J. & Suarez, J.M.S., 2020. "A deformed derivative model for turbulent diffusion of contaminants in the atmosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    6. Balankin, Alexander S. & Bory-Reyes, Juan & Shapiro, Michael, 2016. "Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 345-359.
    7. Rosa, Wanderson & Weberszpil, José, 2018. "Dual conformable derivative: Definition, simple properties and perspectives for applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 137-141.
    8. Zhokh, Alexey & Strizhak, Peter, 2018. "Thiele modulus having regard to the anomalous diffusion in a catalyst pellet," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 58-63.
    9. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.

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