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A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

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  • D. Baleanu
  • A. H. Bhrawy
  • T. M. Taha

Abstract

This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomials Li(α,β)(x) with x ∈ Λ = (0, ∞), α > −1, and β > 0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre‐Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.

Suggested Citation

  • D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:413529
    DOI: 10.1155/2013/413529
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    References listed on IDEAS

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    1. Ali Ahmadian & Mohamed Suleiman & Soheil Salahshour, 2013. "An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-29, June.
    2. Junqiang Song & Fukang Yin & Xiaoqun Cao & Fengshun Lu, 2013. "Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Ali Ahmadian & Mohamed Suleiman & Soheil Salahshour, 2013. "An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional‐Order Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Junqiang Song & Fukang Yin & Xiaoqun Cao & Fengshun Lu, 2013. "Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, February.
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    Citations

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    Cited by:

    1. Ali H. Bhrawy & Abdulrahim AlZahrani & Dumitru Baleanu & Yahia Alhamed, 2014. "A Modified Generalized Laguerre‐Gauss Collocation Method for Fractional Neutral Functional‐Differential Equations on the Half‐Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. M. M. Tharwat & S. M. Al-Harbi, 2013. "Approximation of Eigenvalues of Sturm‐Liouville Problems by Using Hermite Interpolation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Ali Ahmadian & Norazak Senu & Farhad Larki & Soheil Salahshour & Mohamed Suleiman & Md. Shabiul Islam, 2013. "Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. A. H. Bhrawy, 2013. "A New Numerical Algorithm for Solving a Class of Fractional Advection‐Dispersion Equation with Variable Coefficients Using Jacobi Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. A. H. Bhrawy & M. A. Alghamdi, 2013. "Approximate Solutions of Fisher′s Type Equations with Variable Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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