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An efficient method for solving fractional Sturm–Liouville problems

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  • Al-Mdallal, Qasem M.

Abstract

The numerical approximation of the eigenvalues and the eigenfunctions of the fractional Sturm–Liouville problems, in which the second order derivative is replaced by a fractional derivative, is considered. The present results can be implemented on the numerical solution of the fractional diffusion-wave equation. The results show the simplicity and efficiency of the numerical method.

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  • Al-Mdallal, Qasem M., 2009. "An efficient method for solving fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 183-189.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:183-189
    DOI: 10.1016/j.chaos.2007.07.041
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    References listed on IDEAS

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    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    2. Ahmad, Wajdi M. & El-Khazali, Reyad, 2007. "Fractional-order dynamical models of love," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1367-1375.
    3. El-Wakil, S.A. & Abdou, M.A., 2007. "New applications of Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 513-522.
    4. Liang, Y.S. & Su, W.Y., 2007. "The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 682-692.
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    Cited by:

    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. 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.
    3. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    5. Goel, Eti & Pandey, Rajesh K. & Yadav, S. & Agrawal, Om P., 2023. "A numerical approximation for generalized fractional Sturm–Liouville problem with application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 417-436.
    6. He, Ying & Zuo, Qian, 2021. "Jacobi-Davidson method for the second order fractional eigenvalue problems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. 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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