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Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

Author

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  • Želi, Velibor
  • Zorica, Dušan

Abstract

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams–Bashforth and Grünwald–Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Suggested Citation

  • Želi, Velibor & Zorica, Dušan, 2018. "Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2316-2335.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:2316-2335
    DOI: 10.1016/j.physa.2017.11.150
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    Citations

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    Cited by:

    1. Ji Lin & Sergiy Reutskiy & Yuhui Zhang & Yu Sun & Jun Lu, 2023. "The Novel Analytical–Numerical Method for Multi-Dimensional Multi-Term Time-Fractional Equations with General Boundary Conditions," Mathematics, MDPI, vol. 11(4), pages 1-26, February.
    2. Awad, Emad, 2019. "On the time-fractional Cattaneo equation of distributed order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 210-233.
    3. Makhmud A. Sadybekov & Irina N. Pankratova, 2022. "Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions," Mathematics, MDPI, vol. 10(20), pages 1-17, October.

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