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Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection–diffusion equation

Author

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  • Abbasbandy, Saeid
  • Kazem, Saeed
  • Alhuthali, Mohammed S.
  • Alsulami, Hamed H.

Abstract

In this paper, the application of the operational matrix of fractional-order Legendre functions (FLFs) to solve the time-fractional convection–diffusion equation has been investigated. Fractional calculus has been applied to model the engineering and physical processes which are best described with other mathematical tools. The time variable of the time-fractional convection–diffusion equation and its space variable have been approximated by FLFs and shifted Legendre polynomials, respectively. The fractional derivatives together with product matrices of FLFs are employed to convert the solution of this problem to the solution of a system of algebraic equations.

Suggested Citation

  • Abbasbandy, Saeid & Kazem, Saeed & Alhuthali, Mohammed S. & Alsulami, Hamed H., 2015. "Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 31-40.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:31-40
    DOI: 10.1016/j.amc.2015.05.003
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    Citations

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    Cited by:

    1. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
    2. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Behroozifar, M. & Sazmand, A., 2017. "An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 1-17.
    4. Sun, Lin & Chen, Yiming & Dang, Rongqi & Cheng, Gang & Xie, Jiaquan, 2022. "Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 190-203.
    5. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    6. Mohammad Abolhasani & Saeid Abbasbandy & Tofigh Allahviranloo, 2017. "A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains," Mathematics, MDPI, vol. 5(2), pages 1-15, May.

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