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Legendre approximation method for computing eigenvalues of fourth order fractional Sturm–Liouville problem

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  • Aghazadeh, A.
  • Mahmoudi, Y.
  • Saei, F.D.

Abstract

In this paper, a special class of fractional Sturm–Liouville problems of order α (3<α≤4) is discussed. The method is based on utilizing the shifted Legendre polynomials on the interval [0,L] to find numerical approximations for eigenvalues and corresponding eigenfunctions. The proposed method is implemented on several numerical examples. The numerical results indicate the high performance of the method, its effectiveness, and its simplicity in use.

Suggested Citation

  • Aghazadeh, A. & Mahmoudi, Y. & Saei, F.D., 2023. "Legendre approximation method for computing eigenvalues of fourth order fractional Sturm–Liouville problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 286-301.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:286-301
    DOI: 10.1016/j.matcom.2022.11.007
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    References listed on IDEAS

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    1. Kashfi Sadabad, Mahnaz & Jodayree Akbarfam, Aliasghar, 2021. "An efficient numerical method for estimating eigenvalues and eigenfunctions of fractional Sturm–Liouville problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 547-569.
    2. Al-Mdallal, Qasem M. & Syam, Muhammed I., 2014. "The Chebyshev collocation-path following method for solving sixth-order Sturm–Liouville problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 391-398.
    3. Al-Mdallal, Qasem M., 2009. "An efficient method for solving fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 183-189.
    4. Zhang, Maozhu & Li, Kun, 2020. "Dependence of eigenvalues of Sturm–Liouville problems with eigenparameter dependent boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    5. Syam, Muhammed I. & Siyyam, Hani I., 2009. "An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 659-665.
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