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Diffusion process modeling by using fractional-order models

Author

Listed:
  • Sierociuk, Dominik
  • Skovranek, Tomas
  • Macias, Michal
  • Podlubny, Igor
  • Petras, Ivo
  • Dzielinski, Andrzej
  • Ziubinski, Pawel

Abstract

This paper deals with a concept and description of a RC network as an electro-analog model of diffusion process which enables to simulate heat dissipation under different initial and boundary conditions. It is based on well-known analogy between heat and electrical conduction. In the paper are compared analytical solution together with numerical solution and experimentally measured data. For the first time a fractional order model of diffusion process and its modeling via lumped RC network has been used. Simple examples of simulations, measurements and their comparison are shown.

Suggested Citation

  • Sierociuk, Dominik & Skovranek, Tomas & Macias, Michal & Podlubny, Igor & Petras, Ivo & Dzielinski, Andrzej & Ziubinski, Pawel, 2015. "Diffusion process modeling by using fractional-order models," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 2-11.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:2-11
    DOI: 10.1016/j.amc.2014.11.028
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    Citations

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    Cited by:

    1. Ertuğrul Karaçuha & Vasil Tabatadze & Kamil Karaçuha & Nisa Özge Önal & Esra Ergün, 2020. "Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    2. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    3. Krzysztof Oprzędkiewicz & Wojciech Mitkowski & Maciej Rosół, 2021. "Fractional Order Model of the Two Dimensional Heat Transfer Process," Energies, MDPI, vol. 14(19), pages 1-16, October.
    4. Abro, Kashif Ali & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2019. "Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 40-45.
    5. Agarwal, Ritu & Kritika, & Purohit, Sunil Dutt, 2021. "Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    7. Chen, Yuquan & Gao, Qing & Wei, Yiheng & Wang, Yong, 2017. "Study on fractional order gradient methods," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 310-321.
    8. Sowa, Marcin, 2018. "Application of SubIval in solving initial value problems with fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 86-103.
    9. Zhang, Shuo & Liu, Lu & Xue, Dingyu, 2020. "Nyquist-based stability analysis of non-commensurate fractional-order delay systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    10. repec:taf:tsysxx:v:48:y:2017:i:7:p:1460-1471 is not listed on IDEAS

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