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A novel finite difference-spectral method for fractal mobile/immobiletransport model based on Caputo–Fabrizio derivative

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  • Fardi, Mojtaba
  • Khan, Yasir

Abstract

This paper proposes a finite difference-spectral method toa mobile/immobile fractal transport model formulated with the concept of a fractional derivative of Caputo–Fabrizio. A finite difference scheme is used in temporal space to achieve a semi-discrete configuration, whereas a Legendre-spectral approach proposes for spatial discretization. The error calculation of the new procedure is calculated based on the theoretical foundation of the current technique. Finally, a variety of numerical examples are presented to determine the feasibility and applicability of the suggested method in terms of convergence ratio and accuracy.

Suggested Citation

  • Fardi, Mojtaba & Khan, Yasir, 2021. "A novel finite difference-spectral method for fractal mobile/immobiletransport model based on Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309644
    DOI: 10.1016/j.chaos.2020.110573
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    References listed on IDEAS

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    1. Doungmo Goufo, Emile F. & Kumar, Sunil & Mugisha, S.B., 2020. "Similarities in a fifth-order evolution equation with and with no singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    3. Ahmad, Hijaz & Seadawy, Aly R. & Khan, Tufail A., 2020. "Study on numerical solution of dispersive water wave phenomena by using a reliable modification of variational iteration algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 13-23.
    4. Hijaz Ahmad & Tufail A. Khan & Predrag S. Stanimirović & Yu-Ming Chu & Imtiaz Ahmad, 2020. "Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models," Complexity, Hindawi, vol. 2020, pages 1-14, October.
    5. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
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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. El-Tantawy, S.A. & Salas, Alvaro H. & Alharthi, M.R., 2021. "Novel analytical cnoidal and solitary wave solutions of the Extended Kawahara equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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