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Fractional-order Legendre-collocation method for solving fractional initial value problems

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  • Al-Mdallal, Qasem M.
  • Abu Omer, Ahmed S.

Abstract

In this paper, we present a numerical algorithm for solving second-order fractional initial value problems. This numerical algorithm is based on a fractional Legendre-collocation spectral method. The governing fractional differential equation is converted into a nonlinear system of algebraic equations. The error analysis of the proposed numerical algorithm is presented. Comparisons with other numerical methods shows that the proposed algorithm is more accurate and simpler to implement. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.

Suggested Citation

  • Al-Mdallal, Qasem M. & Abu Omer, Ahmed S., 2018. "Fractional-order Legendre-collocation method for solving fractional initial value problems," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 74-84.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:74-84
    DOI: 10.1016/j.amc.2017.10.012
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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Kashkari, Bothayna S.H. & Syam, Muhammed I., 2016. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 281-291.
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    Cited by:

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    6. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
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    10. Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
    11. Karaagac, Berat, 2019. "A study on fractional Klein Gordon equation with non-local and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 218-229.
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    13. Al-Mdallal, Qasem M., 2018. "On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 261-267.

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