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A class of computational approaches for simulating fractional functional differential equations via Dickson polynomials

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  • Panj-Mini, H.
  • Parsa Moghaddam, B.
  • Hashemizadeh, E.

Abstract

In this paper, a new class of computational techniques for the numerical solution of fractional functional differential equations is discussed. The proposed technique is based on Dickson polynomials with which well-known polynomials such as Fibonacci, Lucas and Chebyshev polynomials are related with some parameters. In general, the proposed combined scheme is improved by the fractional Dickson-Tau collocation technique in which a Dickson operation matrix is constructed for fractional differentiation. Then, a genetic algorithm is used to tune the unknown parameters of the proposed methods. Moreover, the error estimates and convergence of the proposed scheme are analysed. The significance of the accuracy and low computational time of the proposed scheme is verified in several numerical examples.

Suggested Citation

  • Panj-Mini, H. & Parsa Moghaddam, B. & Hashemizadeh, E., 2021. "A class of computational approaches for simulating fractional functional differential equations via Dickson polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s096007792100761x
    DOI: 10.1016/j.chaos.2021.111407
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    References listed on IDEAS

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    1. Abdelkawy, M.A. & Lopes, António M. & Babatin, Mohammed M., 2020. "Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    3. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    4. Agarwal, P. & El-Sayed, A.A., 2018. "Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 40-49.
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