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Memory-dependent derivative versus fractional derivative (II): Remodelling diffusion process

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  • Wang, Jin-Liang
  • Li, Hui-Feng

Abstract

The memory-dependent derivative (MDD) is a new substitution for the fractional derivative (FD). It reflects the memory effect in a more distinct way. As an application, the representative heat diffusion process is remodeled with it. In fact, due to the existence of heat-conduction paradox, the time-space evolution mechanisms of this process are challenges to the modelers. The paradox cann’t be ascribed to the classical Fourier law, and the results show that the newly-constructed temporal MDD model is more reasonable than the Maxwell-Cattaneo, the temporal FD, the spatial FD and the common ones. Moreover, different mediums may accord with different memory times and weighted functions. This freedom of choice reflects the flexibility of MDD in modelling. It can be borrowed for exploring other diffusion problems.

Suggested Citation

  • Wang, Jin-Liang & Li, Hui-Feng, 2021. "Memory-dependent derivative versus fractional derivative (II): Remodelling diffusion process," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320305816
    DOI: 10.1016/j.amc.2020.125627
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    References listed on IDEAS

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    1. Zhao, Jingjun & Zhang, Yanming & Xu, Yang, 2020. "Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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    Cited by:

    1. Abouelregal, Ahmed E. & Mohammed, Fawzy A. & Benhamed, Moez & Zakria, Adam & Ahmed, Ibrahim-Elkhalil, 2022. "Vibrations of axially excited rotating micro-beams heated by a high-intensity laser in light of a thermo-elastic model including the memory-dependent derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 81-99.
    2. Rana Yousif & Aref Jeribi & Saad Al-Azzawi, 2023. "Fractional-Order SEIRD Model for Global COVID-19 Outbreak," Mathematics, MDPI, vol. 11(4), pages 1-19, February.

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