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On a Generalized Laguerre Operational Matrix of Fractional Integration

Author

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  • A. H. Bhrawy
  • D. Baleanu
  • L. M. Assas
  • J. A. Tenreiro Machado

Abstract

A new operational matrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived. The fractional integration is described in the Riemann-Liouville sense. This operational matrix is applied together with generalized Laguerre tau method for solving general linear multiterm fractional differential equations (FDEs). The method has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposed method is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Suggested Citation

  • A. H. Bhrawy & D. Baleanu & L. M. Assas & J. A. Tenreiro Machado, 2013. "On a Generalized Laguerre Operational Matrix of Fractional Integration," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
    • Handle: RePEc:hin:jnlmpe:569286
    DOI: 10.1155/2013/569286
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    Cited by:

    1. Guimarães, O. & Labecca, W. & Piqueira, José R.C., 2022. "Solving 2nd order BVPs in planar irregular domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 1-22.
    2. Kumar, S. & Das, Subir & Ong, S.H., 2021. "Analysis of tumor cells in the absence and presence of chemotherapeutic treatment: The case of Caputo-Fabrizio time fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1-14.
    3. Bambe Moutsinga, Claude Rodrigue & Pindza, Edson & Maré, Eben, 2021. "Comparative performance of time spectral methods for solving hyperchaotic finance and cryptocurrency systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Kumar, Sachin & Nieto, Juan J. & Ahmad, Bashir, 2022. "Chebyshev spectral method for solving fuzzy fractional Fredholm–Volterra integro-differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 501-513.

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