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Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system

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  • Heydari, M.H.
  • Razzaghi, M.
  • Avazzadeh, Z.

Abstract

In this paper, a novel fractal-fractional derivative operator with Mittag-Leffler function as its kernel is introduced. Using this differentiation, the fractal-fractional model of the coupled nonlinear Schrödinger-Boussinesq system is defined. The orthonormal shifted discrete Chebyshev polynomials are generated and used for constructing a computational matrix method to solve the defined system. In the established method, using the matrices of the ordinary and fractal-fractional differentiations of these polynomials, the fractal-fractional system transformed into a system of algebraic equations, which is solved readily. Practicability and precision of the method are examined by solving two numerical examples.

Suggested Citation

  • Heydari, M.H. & Razzaghi, M. & Avazzadeh, Z., 2021. "Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309619
    DOI: 10.1016/j.chaos.2020.110570
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    1. Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
    2. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
    3. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    5. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. Xiao-Jun Yang & Dumitru Baleanu & J. A. Tenreiro Machado, 2013. "Systems of Navier-Stokes Equations on Cantor Sets," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, June.
    7. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
    9. Srivastava, H.M. & Saad, Khaled M. & Khader, M.M., 2020. "An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-7, June.
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