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Fractal calculus for modeling electrochemical capacitors under dynamical cycling

ABSTRACT
The differential model for electrochemical capacitors under dynamical cycling results in discontinuity of the electric current. This paradox makes theoretical analysis of the electrochemical capacitors much difficult, and there is not universal approach to treatment of the problem. This paper finds that the fractal calculus can be powerfully applied to the problem, and a continuous electric current can be obtained as it should be.
KEYWORDS
PAPER SUBMITTED: 2020-03-08
PAPER REVISED: 2020-06-15
PAPER ACCEPTED: 2020-06-15
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200308028L
REFERENCES
  1. Zaccagnini, P., et al. Modeling of electrochemical capacitors under dynamical cycling. Electrochimica Acta, 296(2019): 709-718.
  2. Wang, H., Dai, H. Strongly coupled inorganic-nano-carbon hybrid materials for energy storage, Chem. Soc. Rev., 42 (2013):3088-3113
  3. Arico, A.S., et al. Nanostructured materials for advanced energy conversion and storage devices, Nature Materials, 4(5)(2005): 366-377
  4. Stoller, M.D., et al. Graphene-Based Ultracapacitors, Nano Letters, 8(2008), 10, pp.3498-3502
  5. Li, X., et al. Stable RuO2-based ternary composite electrode of sandwiched framework for electrochemicalcapacitors, Electrochimica Acta, 289(2018): 292-310
  6. Priyadharsini, N., et al. Morphology-dependent electrochemical properties of sol-gel synthesized LiCoPO4 for aqueous hybrid capacitors, Electrochimica Acta, 289(2018): 516-526
  7. Li, R. B., et al. Facile synthesis of hierarchical mesoporous beta-manganese dioxide nanoflowers with extremely high specific surface areas for high-performance electrochemical capacitors, Electrochimica Acta, 284(2018): 52-59
  8. Peng, N. B., et al. A Rachford-Rice like equation for solvent evaporation in the bubble electrospinning, Thermal Science, 22(4)(2018): 1679-1683
  9. Tian, D.& He, J.-H. Macromolecular electrospinning: Basic concept & preliminary experiment, Results in Physics, 11( 2018 ):740-742.
  10. Yin, J., et al. Numerical approach to high-throughput of nanofibers by a modified bubble-electrospinning, Thermal Science, 24(2020), 4, pp.2367-2375
  11. Ahmed, A. and Xu, L. Numerical analysis of the electrospinning process for fabrication of composite fibers, Thermal Science, 24(2020), 4, pp.2377-2383
  12. Li, X.X., et al. Nanofibers membrane for detecting heavy metal ions, Thermal Science, 24(2020), 4, pp.2463-2468
  13. Li XX, et al. The effect of sonic vibration on electrospun fiber mats, Journal of Low Frequency Noise Vibration and Active Control, 38(2019),3-4, pp. 1251-1246
  14. Wu, Y.K. & Liu, Y. Fractal-like multiple jets in electrospinning process, Thermal Science, 24(2020), 4, pp.2499-2505
  15. He JH. Advances in Bubble Electrospinning, Recent Patents on Nanotechnology, 13(2019), 3, pp.162 -163
  16. He JH, Ain QT. New promises and future challenges of fractal calculus: from two-scale Thermodynamics to fractal variational principle, Thermal Science, 24(2020),2A, pp. 659-681
  17. He, J.H. Fractal calculus and its geometrical explanation, Results in Physics, 10(2018), 272-276
  18. Li, X.-X., et al. A fractal modification of the surface coverage model for an electrochemical arsenic sensor, Electrochimica Acta,296(2019), pp. 491-493
  19. Wang, Q. L., et al. Fractal calculus and its application to explanation of biomechanism of polar bear hairs, Fractals,26(6)(2018) 1850086
  20. He JH. A short review on analytical methods for to a fully fourth-order nonlinear integral boundary value problem with fractal derivatives, International Journal of Numerical Methods for Heat and Fluid Flow, 2020, DOI (10.1108/HFF-01-2020-0060)
  21. Shen, Y., & He, J.H. Variational principle for a generalized KdV equation in a fractal space, Fractals. 2020, doi.org/10.1142/S0218348X20500693
  22. Wu, Y., He, J.H., Homotopy perturbation method for nonlinear oscillators with coordinate dependent mass. Results in Physics 2018; 10: 270-271.
  23. He, J.H., Homotopy Perturbation Method with an Auxiliary Term. Abstract and Applied Analysis 2012; article number 857612.
  24. He, J.H., Homotopy perturbation method with two expanding parameters. Indian Journal of Physics 2014; 88: 193-196.
  25. Liu, Z.J., et al. Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations. Thermal Science 2017; 21: 1843-1846.
  26. Li, X.X., He, C.H., Homotopy perturbation method coupled with the enhanced perturbation method, Journal of Low Frequency Noise, Vibration & Active Control, 38(2019),3-4, pp. 1399-1403
  27. He, J.H., Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 2006; 20: 1141-1199
  28. Yu, D. N., et al. Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators, Journal of Low Frequency Noise, Vibration & Active Control, 38(2019),3-4, pp. 1554-1540